United chief executive David Gill had been in discussions with Tevez's advisor, Kia Joorabchian, with the aim of keeping the popular Argentine forward.
However, despite the offer of a lucrative five-year contract, that would have made Tevez one of the highest paid players at the club, the South American has decided to leave.
'Benzema likely to leave'A club statement read: "Following contact received from Carlos Tevez's advisors last night, in advance of the deadline the club set for concluding negotiations, Manchester United announces that Carlos will not be signing a new contract with the club.
"The club agreed to pay the option price of £25.5m and offered Carlos a five-year contract which would have made him one of its highest paid players.
"Disappointingly however, his advisors informed the club that, despite the success he has enjoyed during one of the club's most successful periods, he does not wish to continue playing for Manchester United.
"The club would like to thank Carlos for his services over the last two seasons and wishes him good luck for the future."
Tevez's refusal to stay at United will no doubt spark a bidding war between Chelsea, Manchester City and Real Madrid, who have all been linked with the Argentina international.
City are the favourites to confirm Tevez's capture, having made Joorabchian an offer said to be well in excess of United's.
And as Mark Hughes' men are on the verge of confirming Roque Santa Cruz's £18m arrival from Blackburn, it would represent a major statement of intent for a club also hoping to tie up the signing of Barcelona striker Samuel Eto'o.
It leaves United manager Sir Alex Ferguson with a major rebuilding job in attack, given he is still to secure a replacement for Cristiano Ronaldo.
Karim Benzema and Franck Ribery have both been spoken of as potential targets, although there is no guarantee either will come.
And while Antonio Valencia's £18m arrival from Wigan should eventually go through, he is not a proven goalscorer.