With Chelsea having wrapped up the title Friday and Sunderland and Middlesbrough already relegated, the final flurry of matches will decide which two clubs join the champion and second-placed Tottenham Hotspur in the Champions League and which becomes the third side to slide through the trapdoor.
"The 58-times capped Argentina global is out of contract in the summer and has informed the club he will move to pastures new, but leave behind many happy memories", the statement added.
City manager Pep Guardiola's decision to leave fit-again top scorer Sergio Aguero on the bench raised eyebrows, but his unchanged line-up overcame Leicester's early resistance to score twice before half-time.
Toure, along with Jesus Navas, Gael Clichy, Bacary Sagna, Willy Caballero, and Tosin Adarabioyo, may find out only during the offseason.
Guardiola's City took the lead in contentious circumstances in the 29th minute at the Etihad Stadium.
Meanwhile, Manchester City winger Sterling is excited that his team were able to get past Leicester City on Saturday.
"Pablo is a real legend in what he has done in this club", he said. That's why Pablo Zabaleta, in these kind of things, is so, so important.
Jamie Vardy also had a late chance for Leicester who sensed City's nervousness, but the hosts hung on to stay on course for a top-four finish with two games left. "We have to look after our boots". Of the current City players, only Joe Hart and captain Vincent Kompany have been there longer. I remember at that time [Sir Alex] Ferguson and the "noisy neighbours" and this is something that I have been since that time! The two lads we're talking about, I've found them smashing people - really good football people, down to earth, genuine.
His side have two games to clinch the eighth place they have held for much of the season.
"There's always been talent at City even when it was a mid-table club.I reckon what we brought in - because we were young then - was a lot of hunger to go that extra step".
"We have many possibilities", he said.
"If you need to go to war in the big games, you know you've got Zaba with you".
Having invested so much effort in recruiting Guardiola - they first approached him in 2012 before finally landing their man past year - it is unthinkable City would wield the axe so soon.
Swansea's players paid for the tickets of the 3,000 away fans, and the traveling contingent saw their team notch a third win in four games.