Ozil's expiring Arsenal contract has put him on course to become a free agent at the end of the season and United have been heavily linked with a swoop for the World Cup winner.
Just last week there was speculation that Ozil had already started telling Arsenal team-mates that he would be joining United, although it remains unclear if the alleged interest is reciprocal.
But if Ozil really does join United, Silvestre, a five-time Premier League champion during his nine year spell in Manchester, sees a problem with the German's style of play, even though he would be reuniting with Jose Mourinho, a coach who knows him well from their time at Real Madrid.
"I think he would have to change his attitude. I think it's mainly when the team loses the ball," Silvestre told beIN SPORTS this week.
"The first few seconds in reaction is when the coaches want you to get up and try to recover as quickly as possible. Be that man to block and try to stop your opponent.
"And his transitions - sometimes, he looks like 'okay we lost the ball now and I've got to run back now because I'm Arsenal', but sometimes it doesn't look like he is interested, so at United he wouldn't last long - especially with Jose."
Others have famously fallen foul of Mourinho for a lack of defensive effort, notably Juan Mata at Chelsea, while Henrikh Mkhitaryan works harder defensively now than he did when he first joined the club from Borussia Dortmund last summer.
Silvestre also puts the presence of those two creative types down as another reason why United don't really need Ozil in the first place.
"If you put players into categories, I would put him in the with Mkhitaryan and Mata, so you already have two players like this," the ex-France international, also briefly of Arsenal, explained.
"Technical, good vision, proper playmakers. So why would you sign another? You don't need to stockpile these types of players."