The Citizens are believed to be in talks with Chelsea over the proposed sale of Ake this summer, with one report claiming that the Dutchman has already agreed personal terms to return to Stamford Bridge.
According to journalist Fabrizio Romano, City will look to sign a new centre-back this summer if they agree to sell Ake, and Gvardiol is on their radar.
Romano adds that the 20-year-old Croatia international is highly rated by the Premier League champions, although Leipzig are keen to keep hold of the left-footed defender who only joined the German club in 2020.
After a year on loan with Dinamo Zagreb, Gvardiol enjoyed an impressive first season with Leipzig in 2021-22, making 45 appearances across all competitions as well as helping the club win the DFB-Pokal and reach the Europa League semi-finals.
Gvardiol, who still has four years remaining on his Leipzig contract, has also caught the eye of a number of other top European clubs, having previously been linked with the likes of Chelsea, Tottenham Hotspur and Manchester United.
Man City are also understood to have joined Chelsea and Barcelona in the race to sign Sevilla centre-back Jules Kounde, who is allegedly keen to leave the La Liga outfit this summer.