Benjani has been linked with a move to Sunderland and could be the second striker to move on in a matter of days after Robinho sealed a loan move to Santos in his native Brazil.
Even though Roque Santa Cruz remains absent with a calf injury, Mancini believes he has enough cover to cope.
On Benjani, Mancini said: "I spoke with him two days ago and he told me he had a possibility to go and play.
"We have a lot of strikers but he it is up to him to decide.
"If he wants to stay here I will be happy. He is a good player and a good man."