The 30-year-old defender moved to the Etihad Stadium in 2009, signing from Everton in a £22million deal, but has fallen down the first-team pecking order following the emergence of Matija Nastasic in 2012/13.
Manuel Pellegrini's arrival has given Lescott fresh hope of a return to the fold, but is seeking assurances from his new manager that he remains part of his plans.
The England international will hold emergency talks with the Chilean coach when he reports for pre-season training with Manchester City next week, and depending on the outcome could push for a move away this transfer window.
"The situation is simple really," a source told the Daily Star. "He wants to play and doesn't want to spend next season sat on the bench.
"If he isn't going to play regularly at City, then he can go to another club that will value him more."
Gunners boss Arsene Wenger is eager to strengthen his defensive options at the Emirates Stadium this summer, and would be keen to recruit Lescott should he become available.
With just over 12 months remaining on his current contract, the centre-back could be bought for as little as £5million, though his existing wages of £90,000-a-week might prove to be a problem for Arsenal.
In addition to Lescott's extravagant demands another stumbling block would be the rival competition for his signature, with Aston Villa and West Ham both also monitoring the player's situation.