The Dutchman has taken temporary charge of the team since Erik ten Hag’s sacking.
While Van Nistelrooy is only in charge until November 11th, when Ruben Amorim takes over, Shearer believes he can go on to have a successful head coaching career.
Speaking to Betfair, Shearer said: "There are so many factors to that which we don't know. Ruud is a number one. He's a manager and he's managed before, he's had a taste of it again against Leicester on Wednesday and whether he gets the same again this weekend, we don't know. But I suspect, at some stage, that he'll want to go and be a manager himself again.
"Whether he wants to do that now or whether he's prepared to wait and be a coach again for a period of time, we don't know because he was offered jobs before.
"He was in for the Burnley job so it's clear that he wants to be a manager, it's just a matter of when again and whether Amorim is bringing in all his own staff in. Those are all questions that we don't know the answers to."