The Blues will sign at least two new centre-backs during this summer's transfer window, as both Antonio Rudiger and Andreas Christensen have left the club on free transfers.
Juventus's Matthijs de Ligt continues to be linked with a switch to Stamford Bridge, but Bayern Munich are now thought to be in a strong position to sign the Netherlands international.
Talk of a potential return to Chelsea for Ake has gathered pace in recent days, and according to The Times, the Blues are in advanced discussions with Man City over the 27-year-old.
The report claims that the two sides are yet to agree a price, but there have been talks over a transfer, while personal terms have also been discussed.
Ake initially made the move to Chelsea from Feyenoord in 2011, but he found it difficult to make the breakthrough at Stamford Bridge, featuring on just 17 occasions in all competitions.
The defender had loan spells with Reading, Watford and Bournemouth during his time with the Blues before moving to the latter on a permanent basis in 2017.
After three successful seasons with the Cherries in the Premier League, Man City paid in the region of £41m to bring the Dutchman to Manchester.
Ake has won two Premier League titles and the League Cup during his time at Etihad Stadium, but he has largely found it difficult to secure a regular run in the side.
The Dutchman made 27 appearances in all competitions during the 2021-22 campaign but just 14 of those outings were in the Premier League.
Ake was also an unused substitute for both legs of Man City's Champions League semi-final with Real Madrid, while he was overlooked in the latter stages of the season despite defensive injuries for the Citizens.
In total, the defender has made 40 appearances for the Citizens in all competitions, contributing four goals in the process.
Chelsea are yet to make a first-team signing this summer, but the club will also be bringing in a new centre-forward following Romelu Lukaku's return to Inter Milan on loan.
Head coach Thomas Tuchel also needs to make decisions on the futures of a number of loan players, including Conor Gallagher and Armando Broja, who impressed with Crystal Palace and Southampton respectively during the 2021-22 campaign.
Manchester United's Cristiano Ronaldo and Bayern Munich's Robert Lewandowski are said to be forward targets for the Blues, but they will find it difficult to sign either player in the current market.