The Daily Star Sunday says leading contenders Galatasaray pulled the plug when their £6million bid was rejected.
The Turks' chairman Unal Aysal said: "We offered £6m for him but they didn't accept. We cannot give more than this.
"We are not going to follow Nani any more. We cannot afford to pay more than seven million euros for him.
"They want ten million euros - eight million pounds. Because of this, he is not on our transfer targets list any more."
Arsenal chief executive Ivan Gazidis has gone on record as saying the club are willing to splash the cash this summer.
The Portugal ace, 26 is entering the final year of his contract and United have refused to offer him a new deal.