The two former United players are believed to have held a first round of informal discussions with sporting director Jason Wilcox on Tuesday, ahead of United's Premier League match at Burnley. Former United player Darren Fletcher, who is in charge of the Under-18 side, has been named interim head coach and will be in charge for the game.
Fabrizio Romano reported on Tuesday that Solskjaer was close to returning to the club, while Chris Wheeler stated that the Norwegian and Carrick were in a two-way fight for the role, which would see one of them take charge until the end of the season.
It is now being suggested that both Carrick and Solskjaer could feature together in a new backroom team at Old Trafford after Amorim was dismissed on Monday following a reported row with Wilcox last Friday.
If Solskjaer is named as Amorim's successor, it would represent a return to the United hotseat.
The former United and Norway forward initially took charge on an interim basis in December 2018 after the dismissal of Jose Mourinho, before he was appointed full-time the following March.
However, after initially enjoying some success, he was sacked in November 2021 after a downturn in fortunes, with ex-England midfielder Carrick - a member of the coaching team at the time - placed in temporary charge.
United head into the Burnley match sixth in the Premier League, with eight wins from their 20 English top-flight matches so far this season.