United said in June that they were willing to pay the £25.5m to turn the striker's two-year loan move into a permanent five-year deal but Tevez decided to move on.
Speaking after Tevez's decision to leave Manchester United, the player's advisor Kia Joorabchian said: "He has to sign the next five years with a club he believes has got ambition to go forward in the Premier League, a club with history and one that really wants to achieve things."
Argentine international Tevez scored 15 goals last season but was often on the bench for key games and was wary of not getting enough first-team football ahead of the 2010 World Cup in South Africa.
Manchester City's summer spending so far has seen them sign striker Roque Santa Cruz from Blackburn for £18m and Aston Villa midfielder Gareth Barry for £12m.
But a proposed bid for Barcelona striker Samuel Eto'o fell through - even though reports suggested the club was willing to make the Cameroon international the highest-paid player in the world, earning £250,000 per week.
There have also been rumours that Chelsea captain John Terry is on Manchester City's wish-list, although Stamford Bridge boss Carlo Ancelotti insists the England defender is not for sale at any price.
Arsenal striker Emmanuel Adebayor is understood to be in talks over a move to Eastlands.
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