The England international is resigned to the fact he will not be offered a new deal at the Etihad Stadium ahead of next season, but is keen to add to the Premier League and FA Cup winners' medals he has already picked up following his arrival from Everton in 2009.
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The 31-year-old has been on the fringes of Manuel Pellegrini's first team this term but has started every one of the club's Capital One Cup ties and is expected to face Sunderland in Sunday's final at Wembley.
And Lescott has outlined his desire to end his City career with more silverware.
"We are going to be at Wembley for the final, and it's going to be a great occasion and I want to be a part of it," he said. "That was something I thought about in staying and what we could achieve.
"If I can leave having won two league titles and a domestic treble this season, that would be perfect. I've known for a while that the club were not going to renew my contract, but not one performance has been altered by what has been going on with the contract.
"I could have gone in January, but I started the campaign and felt I've played enough games in competitions to warrant my place in the squad and some games in the team."