The Bayern Munich midfielder has publicly stated his desire to play more regular first-team football following a debut campaign which saw opportunities limited, despite the German champions enduring a tumultuous season by their own standards.
Liverpool are keeping tabs on Gravenberch, but their priority targets for midfield remain Khephren Thuram and Manu Kone from Nice and Borussia Monchengladbach respectively.
Both players are 22 years old and likely to be cheaper options than Gravenberch, while also fitting Liverpool's brief of young players who Jurgen Klopp can improve and mould into his style.
The likes of Nicolo Barella, Romeo Lavia and James Ward-Prowse are also thought to be on the Merseyside outfit's midfield shortlist but are considered backup targets at this stage.
The Reds have also reportedly been quoted £51m for Federico Chiesa, while there is allegedly interest in Gambian teenager Adama Bojang, Japanese winger Keito Nakamura and Paris Saint-Germain starlet Warren Zaire-Emery.
In defence, Jurrien Timber remains a target but Liverpool face renewed competition for his signature from Arsenal, while Manchester United are also in the race.
Concrete moves for other rumoured defensive targets such as Josko Gvardiol and Benjamin Pavard are considered unlikely at this stage.
In terms of outgoings, Fabio Carvalho still has plenty of suitors, with West Ham United the latest club to be credited with an interest in a loan move.
Klopp could consider letting the youngster leave on loan for next season, but Liverpool are reluctant to lose him on a permanent basis despite RB Leipzig pushing for such a deal.
PRIORITY POSITIONS
Midfield
Right-back
Centre-back
Liverpool's main priority for this summer's window is undoubtedly to strengthen their midfield, which was ailing for much of last season and which has been further weakened by the departures of Naby Keita, James Milner and Alex Oxlade-Chamberlain at the end of their contracts.
Work has already begun in that department, with Jurgen Klopp's side moving quickly to bring in World Cup winner Alexis Mac Allister from Brighton & Hove Albion for a cut-price fee thought to be worth around £35m initially.
The Argentine is unlikely to be Liverpool's solitary midfield signing of the summer, though, with a host of other players in that area of the pitch being linked with a switch to Anfield.
Right-back is also an area Liverpool could look to add depth with Trent Alexander-Arnold adopting more of a hybrid role towards the latter stages of last season, particularly after Calvin Ramsay left on loan for Preston North End.
DONE DEALS
In
Alexis Mac Allister (£35m, Brighton & Hove Albion)
Out
James Milner (free, Brighton & Hove Albion)
Naby Keita (free, Werder Bremen)
Roberto Firmino (end of contract)
Alex Oxlade-Chamberlain (end of contract)
Calvin Ramsay (loan, Preston North End)
Harvey Davies (loan, Crewe Alexandra)
Leighton Clarkson (undisclosed, Aberdeen)
Liverpool total spent to date: £35m
Liverpool total received to date: £0m
Liverpool net transfer balance: -£35m
TOP TARGETS
Khephren Thuram (Nice)
Age: 22
Position: Midfield
Nationality: French
Valuation: £27.4m (€32m)
Contract expires: June 2025
Rumour strength: Strong
Likelihood of deal: Likely
Manu Kone (Borussia Monchengladbach)
Age: 22
Position: Midfield
Nationality: French
Valuation: £25.7m (€30m)
Contract expires: June 2025
Rumour strength: Strong
Likelihood of deal: Likely
Nicolo Barella (Inter Milan)
Age: 26
Position: Midfield
Nationality: Italian
Valuation: £64.3m (€75m)
Contract expires: June 2026
Rumour strength: Strong
Likelihood of deal: Possible
Jurrien Timber (Ajax)
Age: 21
Position: Defence
Nationality: Dutch
Valuation: £36m (€42m)
Contract expires: June 2025
Rumour strength: Medium
Likelihood of deal: Possible
Ryan Gravenberch (Bayern Munich)
Age: 21
Position: Midfield
Nationality: Dutch
Valuation: £25.7m (€30m)
Contract expires: June 2027
Rumour strength: Medium
Likelihood of deal: Possible
Romeo Lavia (Southampton)
Age: 19
Position: Midfield
Nationality: Belgian
Valuation: £21.4m (€25m)
Contract expires: June 2027
Rumour strength: Medium
Likelihood of deal: Possible
James Ward-Prowse (Southampton)
Age: 28
Position: Midfield
Nationality: English
Valuation: £32.6m (€38m)
Contract expires: June 2026
Rumour strength: Medium
Likelihood of deal: Possible
Conor Gallagher (Chelsea)
Age: 23
Position: Midfield
Nationality: English
Valuation: £27.4m (€32m)
Contract expires: June 2025
Rumour strength: Medium
Likelihood of deal: Possible
Mason Mount (Chelsea)
Age: 24
Position: Midfield
Nationality: English
Valuation: £55.7m (€65m)
Contract expires: June 2024
Rumour strength: Medium
Likelihood of deal: Unlikely
Adama Bojang (Steve Biko FC)
Age: 19
Position: Striker
Nationality: Gambian
Valuation: £128k (€150k)
Contract expires: Unknown
Rumour strength: Medium
Likelihood of deal: Unlikely
Gabri Veiga (Celta Vigo)
Age: 21
Position: Midfield
Nationality: Spanish
Valuation: £25.7m (€30m)
Contract expires: June 2026
Rumour strength: Medium
Likelihood of deal: Unlikely
Franck Kessie (Barcelona)
Age: 26
Position: Midfield
Nationality: Ivorian
Valuation: £21.4m (€25m)
Contract expires: June 2026
Rumour strength: Medium
Likelihood of deal: Unlikely
Josko Gvardiol (RB Leipzig)
Age: 21
Position: Defence
Nationality: Croatian
Valuation: £64.3m (€75m)
Contract expires: June 2027
Rumour strength: Medium
Likelihood of deal: Unlikely
Benjamin Pavard (Bayern Munich)
Age: 27
Position: Defence
Nationality: French
Valuation: £30m (€35m)
Contract expires: June 2024
Rumour strength: Medium
Likelihood of deal: Unlikely
Federico Chiesa (Juventus)
Age: 25
Position: Forward
Nationality: Italian
Valuation: £34.3m (€40m)
Contract expires: June 2025
Rumour strength: Medium
Likelihood of deal: Unlikely
Warren Zaire-Emery (Paris Saint-Germain)
Age: 17
Position: Forward
Nationality: French
Valuation: £15.4m (€18m)
Contract expires: June 2025
Rumour strength: Weak
Likelihood of deal: Unlikely
Keito Nakamura (LASK Linz)
Age: 22
Position: Winger
Nationality: Japanese
Valuation: £6.8m (€8m)
Contract expires: June 2025
Rumour strength: Weak
Likelihood of deal: Unlikely
Levi Colwill (Chelsea)
Age: 20
Position: Defence
Nationality: English
Valuation: £13.7m (€16m)
Contract expires: June 2025
Rumour strength: Weak
Likelihood of deal: Very unlikely
Alex Scott (Bristol City)
Age: 19
Position: Midfield
Nationality: English
Valuation: £17.1m (€20m)
Contract expires: June 2025
Rumour strength: Weak
Likelihood of deal: Very unlikely
Marc Guehi (Crystal Palace)
Age: 22
Position: Defence
Nationality: English
Valuation: £29.9m (€35m)
Contract expires: June 2026
Rumour strength: Weak
Likelihood of deal: Very unlikely
Ruben Neves (Wolverhampton Wanderers)
Age: 26
Position: Midfield
Nationality: Portuguese
Valuation: £34.3m (€40m)
Contract expires: June 2024
Rumour strength: Medium
Likelihood of deal: Very unlikely
Federico Valverde (Real Madrid)
Age: 24
Position: Midfield
Nationality: Uruguayan
Valuation: £85.7m (€100m)
Contract expires: June 2027
Rumour strength: Weak
Likelihood of deal: Very unlikely
Joshua Kimmich (Bayern Munich)
Age: 28
Position: Midfield
Nationality: German
Valuation: £68.5m (€80m)
Contract expires: June 2025
Rumour strength: Weak
Likelihood of deal: Very unlikely
Declan Rice (West Ham United)
Age: 24
Position: Midfield
Nationality: English
Valuation: £68.5m (€80m)
Contract expires: June 2024
Rumour strength: Weak
Likelihood of deal: Very unlikely
Kylian Mbappe (Paris Saint-Germain)
Age: 24
Position: Forward
Nationality: French
Valuation: £153.9m (€180m)
Contract expires: June 2024
Rumour strength: Weak
Likelihood of deal: Very unlikely
POSSIBLE OUTGOINGS
Fabio Carvalho
Age: 20
Position: Midfield
Nationality: English
Valuation: £17.1m (€20m)
Contract expires: June 2027
Rumour strength: Strong
Likelihood of deal: Possible
Interested clubs: RB Leipzig, Burnley, West Ham United, Brentford
CSKA Moscow 
FC Rostov 
Leicester 
Chelsea 
Valencia 
Betis 
Dynamo Kyiv 
Chornomorets Odesa 
Verona 
Inter 
Bayer Leverkusen 
FC Heidenheim 
Borussia Dortmund 
SC Freiburg 
VFL Wolfsburg 
Union Berlin 
Arsenal 
Nottingham Forest 
Everton 
Brentford 
Spartak Moscow 
Lokomotiv Moscow 
Rangers 
Dundee Utd 
Atletico Madrid 
Alaves 
Lens 
Marseille 
Ingulets Petrove 
Shakhtar Donetsk 
AC Milan 
Juventus 
ST Malo 
Bordeaux 
Manchester City 
Tottenham 
Eintracht Frankfurt 
Werder Bremen 
Girona 
Espanyol 
Feyenoord 
Heerenveen 
ST Etienne 
Montpellier 
Grenoble Foot 38 
Heart Of Midlothian 
Celtic 
Reims 
Lyon 
PSV 
Groningen 
Celta Vigo 
Barcelona 
Benfica 
Estrela Da Amadora 
Sparta Rotterdam 
AZ Alkmaar 
Southampton 
Liverpool