Nicky Butt has recalled Carrick telling him he didn't want to return to coaching unless it was for one particular job.
Carrick has endured a dreadful run of form, going nine games without a win, and his position at Old Trafford is under threat.
Nicky Butt, 51, a former Manchester United teammate of Carrick's, said Carrick told him he wasn't interested in coaching unless it was for his old club.
Butt said on "The Good, the Bad & the Football" podcast: "He said, 'No, it's not for me. There's too much going on, my head's all over the place. I'd only do it for the big one, and the big one is Manchester United.'"
The comments caused quite a stir at the time, and Carrick himself later responded to them at a press conference.
Butt has now clarified his remarks, stressing that Carrick would only take a new job if it was with the Red Devils.
Asked about his claim that Carrick didn't want to return to coaching, Butt said on Piers Morgan's "Uncensored" show: "I think I did say that, but let me explain what I meant. I won't back down, I really won't, and I'll make it clear.
"I was playing padel with Carrick, he was my doubles partner, and we were talking about football and Middlesbrough.
"After the match, we had a beer and I said, 'Mate, what are you going to do next? What do you think you'll do when you get back into coaching?'
"He said, 'No, everything's a mess, it's too tiring, but if that big opportunity comes, I'll obviously take it.'"
"That big opportunity did come, and he took it. I wasn't saying Carrick didn't want the Manchester United job. I meant he didn't want just any job.
"He didn't want to drive up and down the M6 all day for nothing, with kids at home to look after.
"But if that big job came along, and I think he meant Manchester United, he would take it. That's what I discussed with him."
Butt then explained why he didn't think Carrick would walk away willingly, no matter how bad the club's situation became.
After the 0-3 defeat to AFC Bournemouth last month, Carrick narrowly survived a crisis meeting, and his time to turn things around in the north-west of England may now be running out.
