It was reported on Wednesday morning that the Spanish winger was close to signing for the Premier League champions in a big-money move.
Cole believes that the flair of a player like Mata is just what United need at the moment in their bid to climb back up the table.
"Jose Mourinho has made his decision why he's not in the team so if he did come to Manchester United I think he'd be a fantastic player for them," the ex-England international told Sky Sports News.
"He's proved his intelligence, not just with Chelsea but also for the national team. He's a quality player with all the attributes. He's very creative and I think that's what Manchester United need right now - some creativity."
United continue their Premier League campaign on Tuesday when they host Cardiff City.