Istanbul-based Gala lodged a £6million bid for the Portugal international on Monday night but United wanted more and they will now abandon their chase for his services.
"We offered seven million euros (£6million) for him," said chairman Unal Aysal. "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 seven million euros for him.
"They want 10 million euros (£8.5million). Because of this he is not on our transfer list anymore."