The former player, who is serving as interim boss for the remainder of the season after Ruben Amorim’s recent sacking, has impressed some, including Daniel Sturridge.
However, Keane dismissed the idea, echoing Gary Neville’s belief that Carrick is not the long-term solution.
"I hope he does really well. There cannot be any consideration that Michael takes the job beyond this season, for Michael and for the club,” he said on Stick to Football.
"If he wins every game, look, we could be sat here in the season where he’s done unbelievably well, and we’re always thinking the fans are up and they’re in the Champions League places, fifth or whatever.
"It could happen if there’s a good run, and we could all be getting swayed with it. I honestly feel like (you have to look at others) at the end of the season when you’ve got (Mauricio) Pochettino, (Thomas) Tuchel, and (Carlo) Ancelotti."