Sterling has told Liverpool manager Brendan Rodgers he wants to leave Anfield to join a club who can offer him Champions League action next season and Man City have made the first move in what could prove a lengthy saga to settle his future.
According to the Times, City's bid valued Sterling at £25m, with an additional £5m to be paid in potential add-ons.
But Liverpool are determined to keep hold of their most gifted youngster and have snubbed the approach for the 20-year-old, who has two years remaining on his current £35,000-a-week contract.
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It is believed that only an astronomical offer of at least £50m could persuade Liverpool to consider letting Sterling leave.
Liverpool remain keen to convince Sterling to sign a new contract, even though he rejected a deal that would have paid him around £100,000-a-week earlier this year.
Sterling’s refusal to commit to Liverpool has angered the club’s supporters, who jeered him at an end of season awards dinner.
The situation turned even uglier when his agent Aidy Ward last month said there was no chance Sterling would extend his contract no matter how much money Liverpool offered.
Liverpool responded by cancelling a scheduled meeting with Sterling and his representative, while Rodgers left the winger on the bench for the team's 6-1 thrashing at Stoke City on the final day of the Premier League season.
City's approach for Sterling is unlikely to be their last since it came just hours after the club's chairman Khaldoon Al Mubarak promised "high-quality" signings and admitted Manuel Pellegrini's team failed to meet expectations during their failed defence of the Premier League title.
Speaking in an interview with City TV, Khaldoon said: “We want a squad that is able and has the capability and quality to win the Premier League, compete and win the Champions League, compete and be able to go all the way in two cup competitions in England.
“I think you will see some changes. You will see some players who have served us well and maybe it is time for them to move to their next challenge, and you will see us in the market bringing high-quality individuals that fit within what we are aspiring to coming in this summer.
“I can assure you the squad will be stronger, the team will be more competitive. I am both confident and excited about what is coming next year.”
Arsenal, Chelsea and Manchester United are also reported to be interested in Sterling, who is currently on international duty with England ahead of their Euro 2016 qualifier in Slovenia on Sunday.
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