The former Liverpool striker has been linked with a move back to the Barclays Premier League in the January transfer window after failing to secure a regular starting role at OM this season.
And Pape Diouf, the president of the Mediterranean club, revealed on Tuesday that City had inquired about the services of Cisse, but that he had turned them down.
"He is wanted, that is for sure," said Diouf. "I myself have been approached by Manchester City (for Cisse's services), but I turned it down categorically."
Diouf insists the 26-year-old is going nowhere.
"I want to be clear - Djibril Cisse will not leave. He will stay at OM until the end of the season," he added.
"I have always wanted to rediscover the Djibril that we signed, the efficient Djibril.
"I have never doubted his abilities, his qualities. He got through difficulties last year and I have no doubt that he will get out of them again this season.
"With everything that he has had to endure, read, see and hear, I understand that it piles the pressure on him to leave, having been contacted by an English club that is among the leading teams in their league.
"But when he and myself discussed this, he understood my position - he understood that I will not let him leave and he has no problem with me."