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.
Another former United star 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.
It is now being suggested both Carrick and Solskjaer could feature 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.
Solskjaer, however, was sacked in November 2021, with ex-England midfielder Carrick 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.