Manchester United are without a win in nine games, their longest run of such since 1988, and leaves the club 17th in the Premier League.
Their last win came back in September against Sabah FK in the Champions League, a game where United were heavy favourites.
United have lost four of their last five matches, including each of their last three and reports state Carrick may be replaced in the international break as the board plan for a future without him.
Carrick will certainly be in the dugout for next weekend’s Premier League game against Aston Villa, but as pressure grows, Solskjaer was asked if he would step back into the role if he got the call.
“Going back to what has been is not always as good. Yes, I had lined up (as Manchester United's interim manager after Amorim’s sacking), but I didn't think it would last longer than the summer. It was probably time for someone else to try.
“I also feel like I have something unresolved. Of course it would have been nice to have the opportunity again.”
He later said: “If Michael does well for 10 years and decides to quit, and they ask me if I can take them for two months, of course I wouldn't say no. I've been at that club for 18-19 years, so it's part of the family. But it's not something I'm thinking about.
“Michael has what it takes to take that club forward. I think he's the right man. He understands the club, understands the fans and knows what's needed."
Solskjaer oversaw 168 competitive matches in total, taking United to a Europa League final and their highest Premier League finish since Sir Alex Ferguson retired.
He also went 29 Premier League away matches unbeaten between January 2020 and October 2021 and despite being sacked, he is objectively one of the best managers United have had since the departure of Sir Alex Ferguson in 2013.