Carrick has had a fantastic start to life with the Red Devils since taking over from Ruben Amorim after winning his opening games against Manchester City and Premier League leaders Arsenal.
Earlier this week, Keane suggested that Carrick should not be considered to take the role full-time once the season was over which sparked controversy amongst supporters who back Carrick.
Now, speaking on The Overlap, Keane has back tracked and hopes Carrick lands the role even if he doesn’t think he is perfect.
"I hope they give it to him," Keane said. "I hope they give it to him in the summer. I don't think it's the right decision, good luck with it.
“Yeah, but, I'm sticking to my guns. I've said my piece, I think that he's got the job, and if he gets it in the summer then you go 'listen, good luck to him'.
"I think you can get a better manager than Carrick, absolutely. But I think he's doing a good job, perfect timing for him, and even if he doesn't get the United job, these results a bit like Ruud (Van Nistelrooy), he can get another job, probably another Premiership manager.
"I think you can get a better manager than Carrick, absolutely. But I think he's doing a good job, perfect timing for him."
Van Nistelrooy left United and ended up taking over as Leicester coach when the side were in the Premier League and Keane suggests Carrick could do the same if it does not work out in the future for the former midfielder who, if his form continues, could stay.