Carrick has emerged as the frontrunner ahead of Ole Gunnar Solskjaer as the Red Devils aim to replace interim manager Darren Fletcher, who took over from former manager Ruben Amorim last week.
Further talks are planned with Carrick and his representatives on Monday according to reports in what looks to be a straight replacement for Fletcher until the end of the season.
As speculation grows, quotes are resurfacing on the former United midfielder as fans ponder if he is good enough to lead the club until the end of the campaign when a permanent manager will be selected.
Ronaldo, who found the net three times under Carrick's tenure when Solskjaer was sacked, backed him to succeed in the future.
"Michael Carrick was a class act as a player, and he can become a great coach as well.
"Nothing is impossible for this guy. Personally, I'm proud to have played with him by my side, as well as with him as a manager on our bench."
Fletcher's tenure began with a 2-2 draw away at Burnley last Wednesday, before his side were knocked out of the FA Cup by Brighton at the weekend.
Carrick, who has managed Middlesbrough before being sacked in June, is edging towards taking the job, where he will aim to lead the side to a finish within the European spots.