The Germany international was left out of the Gunners squad for their 1-0 Premier League defeat to Sheffield United on Monday and was again dropped for Thursday’s Europa League win over Vitoria.
But former United midfielder Scholes believes that the 31-year-old could be just the kind of player Ole Gunnar Solskjaer’s side needs.
The Reds toiled to a 1-0 win over Partizan Belgrade in Serbia on Thursday courtesy of an Anthony Martial penalty, with the goal being their only shot on target.
And with Ozil being increasingly frozen out by Arsenal boss Unai Emery, Scholes thinks he could be a solution for the Old Trafford club.
"Man United could do with someone like Ozil who can link a team together,” he told BT Sport.
"[He is] a player who can link teams together. He has got great quality, he's shown that in his career.
"He could be an answer short-term, I don't know. I think that would be up to him, ultimately.
"I can't [see it happening], but he's the type of player, short-term, who United could do with."
Ozil has made just one Premier League appearances this season for the Emirates club, during the 2-2 draw with Watford on 15 September.
He also featured in the 5-0 win over Nottingham Forest in the League Cup, when he was handed the captain’s armband, but has otherwise been overlooked this term.
The German has a contract in north London until June 2021.
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