Butt, Carrick’s former Manchester United teammate, said on The Good, The Bad & The Football podcast that the current manager had once told him the demands of management had left him questioning whether it was the right career.
According to Butt, Carrick said: “no it's not for me, it's too much, my head's all over the show, I'd only do it for the big job. The big job is Man United.”
Carrick returned to United in January after Ruben Amorim’s departure and guided the club to third place in the Premier League last season. He was subsequently given the permanent role, but has faced a difficult start to the new campaign.
Asked about Butt’s account ahead of the trip to Leeds United, Carrick responded: “I definitely wouldn't be here if that was the case, would I?”
He said the position was the best role he could have and stressed that he felt both the privilege and responsibility of managing his former club.
“I feel a real privilege of being in this position and a real responsibility, but equally a drive of wanting to make a difference and having success here,” Carrick said.
The manager also rejected the idea that the current pressure had made him question his future. Instead, he said difficult periods were part of what motivated him.
“I'm loving it. I love the situation when actually you get some sort of struggle and you've got to find a way out of it. I actually enjoy that because that's part of what drives you to have success.
“If you're not ready for that and you can't do anything that's difficult, then you're never going to be great. So we've got to work our way through it, and I'm enjoying it as we go.”
Carrick’s comments came as United prepared for a meeting with Leeds at Elland Road, where Amorim’s final match as head coach had preceded his departure in January.
United had suffered four defeats in their first nine games of the season, increasing scrutiny of Carrick after the strong finish that secured Champions League qualification last term.
He insisted, however, that his focus was on improving the team rather than protecting his position.
“I don't think about: 'How am I going to get through this? How am I going to survive this? What do I need to do to look after myself?'” he said.
“I really don't take it about me. It's about this football club and winning football matches.”
Carrick added that he did not view the Leeds fixture as a personal last chance, saying he was looking forward to the game and remained determined to move United forward.
“I understand the reality. I accept where we are, but I don't feel that. I'm totally focused on what's best for this football club and what's going to take to win games: get the boys playing how we know we're capable of, and we still don't think we're that far away.
“We can turn a few things in our favour, and we can move forward pretty quickly.”