The former Manchester United manager was approached after Ruben Amorim's departure in January, with the club considering both Solskjaer and his former assistant Carrick for the temporary position. Carrick ultimately got the job, but Solskjaer has now provided his account of the conversations and admitted he would have been willing to help his former club.
"It was a very special period. Of course it was. It was special in many ways," Solskjaer told TV 2.
The Norwegian said he had spoken positively about Carrick during his discussions with United, recognising the qualities of the man who had worked alongside him at Old Trafford between 2018 and 2021.
"When I spoke to United, I praised Michael as well. I said, 'If you choose him, you will get a good man.' I think he did the same for me too," Solskjaer explained.
"Neither of us was desperate to get the job. We would probably both have stepped in if they asked. At that moment, the discussion was about being interim manager until the end of the season."
Solskjaer also rejected reports that he had made demands over the length of a potential contract or sought assurances about a longer-term appointment.
"No, that's just nonsense! I had a good conversation with Jason Wilcox and Omar Berrada. We didn't talk about contract length or anything like that. I was available if needed and I had no demands."
He described the exchange as a conversation rather than a negotiation, adding that he had offered his thoughts on what United needed to do to move forward.
"I gave my input on what needs to happen for the club to move forward. It was one small conversation we had. There were no negotiations."
Although he did not return to the dugout, Solskjaer has not completely closed the door on another opportunity at Old Trafford. He admitted that he still feels he has unfinished business at the club, where he spent 18 years as a player and manager.
"I feel that I have something unfinished. Of course it would have been great to have the opportunity again."
However, he was clear that he believes Carrick is the right person to lead United. The pair remain in regular contact, and Solskjaer has confidence in his former colleague's understanding of the club.
"Michael has what it takes to take that club forward. I think he is the right man. He understands the club, understands the fans and knows what it takes."
Solskjaer, who was dismissed by United in November 2021, has largely kept a low profile since his departure, aside from a brief spell with Besiktas in 2025. Now settled in his hometown of Kristiansund, he told TV 2 that he intends to remain there, even while acknowledging that he would consider another coaching job if the right opportunity arose.
Asked whether he would ever return to United, he offered a hypothetical scenario rather than suggesting he was seeking the position.
"If Michael does well for ten years and decides to stop, and they ask me if I can take them for two months, of course I wouldn't say no. I have 18 or 19 years at that club, so it is part of the family. But it is not something I think about."