The Croatian has impressed in the Bundesliga since making the switch from Dinamo Zagreb in the summer of 2021, playing 87 times for Leipzig, including in the Champions League.
This term the 21-year-old has once again been a key figure for his side, starting 24 Bundesliga matches as the club finished third and secured Champions League football for next term.
Manchester City are not resting on their laurels despite winning a historic treble under Pep Guardiola last season, moving quickly in the transfer market as they aim to maintain an unprecedented level of success for the club.
According to the Daily Mail, the Citizens are set to step up their efforts to bring Gvardiol into their defensive ranks for next season, with the Premier League champions willing to pay £103m for the privilege.
It is understood that the centre-back wishes to leave the German club this summer after a successful two-year spell, while Man City are said to be targeting a replacement for Aymeric Laporte should he depart in this window.
Gvardiol's former club Zagreb reportedly have a 20 per cent sell-on clause on the defender, meaning they could be in for a sizeable chunk of money should the player make the switch to the Premier League.
Reports on Sunday claimed that the Croatian has already agreed personal terms with Guardiola's men after City's director of football Txiki Begiristain met with the player's representatives to discuss a deal.
The Champions League holders are said to be close to completing the signing of fellow Croatian Mateo Kovacic from Chelsea after the midfielder reportedly completed a medical.
A £25m transfer fee paid to the Blues will see the former Real Madrid player move to the Etihad in the next few days according to reports, ending Kovacic five-year stay at Stamford Bridge.
Gvardiol had his season cut short after suffering a groin injury in May, meaning he was unable to play a part for Croatia in their UEFA Nations League clashes against the Netherlands and Spain.
Zlatko Dalic's men were only a penalty shootout away from winning their first-ever major trophy after they played out a goalless 120 minutes against the Spaniards, however Bruno Petkovic and Lovro Majer went on to miss decisive kicks from 12 yards out.
Man City are looking to boost their centre-back ranks with the signing of Gvardiol despite being the Premier League's joint most-stubborn defence last term - only Newcastle United could match City's record of conceding only 33 goals in 38 league fixtures.