The Portuguese winger is thought to be available this summer after a disappointing season, but the Turkish giants have balked at the £8.5m fee the Red Devils are demanding
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The 26-year-old has been with the club since 2007 and has been attracting interest from teams outside the Premier League, including Monaco - though they will have to meet United's price tag.
One club unable to match the Red Devils' valuation is Galatasaray, with the Turkish outfit's chairman Unal Aysal revealing that the club's £6m bid for the winger had been rejected as United hold out for a fee closer to £8.5m.
"We offered 7 million euros (£6m) for him," Aysal told Milliyet. "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 7 million euros for him. They want 10 million euros (£8.5m). Because of this he is not on our transfer list anymore."
Nani made seven starts in the Premier League last season, scoring only once, and was sent off against Real Madrid as United crashed out of the Champions League.