The 27-year-old's long-term future at the Etihad Stadium is believed to be uncertain as he will soon be entering the final year of his contract, while competition for places has intensified following the arrivals of Erling Braut Haaland and Julian Alvarez.
Premier League rivals Chelsea are understood to have stepped up their efforts to sign Sterling this summer, with the Blues set to reinforce their frontline should striker Romelu Lukaku return to Inter Milan.
According to journalist Fabrizio Romano, Chelsea regard Sterling as their primary target this summer and they have seen an opening offer of €25m (£21.4m) plus add-ons rejected by the Premier League champions.
Romano adds that Thomas Tuchel's side are planning to make a second bid for the England international, with Man City valuing the forward between €55m (£47.1m) and €60m (£51.4m).
Since joining the Citizens from Liverpool in 2015, Sterling has recorded 131 goals and 95 assists in 339 appearances across all competitions, winning a total of 12 trophies.
Chelsea are also believed to be interested in signing Sterling's Man City teammate Nathan Ake, who spent time in the West London club's academy and made 17 senior appearances before leaving Stamford Bridge in 2017. body check tags ::