The Portugal international has never really fulfilled his potential at Old Trafford and new boss David Moyes is thought to be ready to sell this summer.
Galatasaray are among the clubs who are interested in signing Nani, who has just one year left on his contract, but claim they cannot meet United's valuation.
The Turkish club's chairman, Unal Aysal, said: "We offered €7million (£6m) for him. But they didn't accept. We can't give more than this.
"We are not going to follow Nani anymore. We can't give more than €7m for him.
"They want €10million (£8.5million). Because of this he is not on our transfer list anymore."