The 19-year-old impressed during his breakout season in the Premier League despite Southampton's relegation to the Championship.
Arsenal and Manchester United are known suitors for the starlet but will have to stump up a sizeable fee for the former Manchester City youngster.
Both clubs are looking to bolster their midfields this summer with a number of stars set to be offloaded.
Mikel Arteta's Gunners are likely to see both Granit Xhaka and Thomas Partey move on this summer, while January signing Jorginho has attracted interest from Serie A champions Napoli.
United, on the other hand, are hoping to add much-needed quality to their midfield as they plot an assault on European and domestic honours next term.
But Southampton view the Lavia as one of their biggest assets as they face up to life in the Championship.
That means a fee of £50m is likely to be the benchmark in any negotiations for the Belgian.
It also takes into consideration clauses inserted in the £12.5m deal that took him from the Etihad Stadium to St. Mary's last summer.
City inserted a clause entitling them to 20 per cent of any future sale meaning they would net £10m should either Arsenal or United meet Saints' asking price.
Most read in Football
Record Rice bid rejected, Arsenal's new Havertz offer, Chelsea announce Nkunku
West Ham to reject second record-breaking bid from Arsenal for Declan Rice
Souness reveals incredible donation from Man United icon Sir Alex after charity swim
Emotional Souness holds back tears over £1m charity swim: 'The money will never be enough'
A sale would hand Southampton a hefty war chest to help reshape their squad ahead of a bid for an instant return to the Premier League.
Lavia made 35 appearances last season for Southampton, 29 of them in the Premier League, and made his debut for Belgium in a friendly against Germany in March.