Arsenal manager Arsene Wenger has also denied reports linking the Gunners with a move for the Portugal international, who has been described as "an incredible talent" by his boss
The Portugal international has made only seven appearances this season and is currently sidelined with a hamstring injury.
But the 70-year-old boss has poured cold water on reports claiming that the midfielder could move clubs in the New Year, describing him as "an incredible talent".
"His contract isn't up for a year and a half," Sir Alex told reporters. "We need Nani. He offers something different from the other players. He's an incredible talent, the boy.
"Unfortunately, he's injured at the moment. We have sent him over to Dubai for a break, to help him in his recovery.
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"He's got a future here. Why would I want to let him go?"
Arsenal manager Arsene Wenger, meanwhile, has dismissed rumours suggesting the north London club could launch a bid for Nani next month.
The Arsenal boss has stated that he is not considering any Manchester United players as January targets, effectively ruling out the possibility of the 26-year-old transferring to the Emirates Stadium.
Asked about the speculation by reporters following his side's 7-3 victory over Newcastle, Wenger replied: "Nani? No.
"We don’t look at any player from United because players are under contract and I don't think they would sell a player during the course of the season. They don't need money."
Since joining United from Sporting Lisbon in 2007, Nani has made 205 first-team appearances for the Red Devils, scoring 38 times in the process.