The 19-year-old came through the youth system at Tromso before making the move to Man United in August 2020 after being linked with Liverpool and Everton.
Hansen-Aaroen is yet to make his first-team debut for the Red Devils, but he has turned out for the club at Under-21s level on 47 occasions, scoring five goals and registering two assists.
This season, the Norwegian has two goals in eight Premier League 2 appearances, while he has also featured twice in the UEFA Youth League.
According to FootballTransfers, having failed to agree fresh terms with Man United, the youngster is preparing to make the move to Werder Bremen before the end of the January transfer window.
The report claims that Hansen-Aaroen is not interested in signing a new deal at Old Trafford, as he wants first-team football at this stage of his career.
The youngster is said to be preparing to travel to Germany for a medical, and all parties are confident that the deal will go through before Thursday night's transfer deadline.
According to the Manchester Evening News, Man United had been hopeful of coming to an agreement with him over a new contract this month.
However, a sale on Thursday is expected to earn them more than any compensation fee that they would be due if he left this summer.
Man United had allegedly been planning to sign Hansen-Aaroen to a new contract before sending him on loan for the second half of the campaign.
Ajax, Atletico Madrid and Napoli are among the clubs said to have shown an interest in him, but he is now set to make the move to the Bundesliga with Bremen.
Hansen-Aaroen is capable of operating in a number of different forward positions, and it had initially been thought that he would be given first-team opportunities by current first-team head coach Erik ten Hag.
Man United's transfer window has been dominated by outgoings, with Facundo Pellistri the latest player to leave, moving on loan to Granada for the second half of the campaign.
The Red Devils are thought to have considered moving for a new striker in the winter market, but the rules surrounding Financial Fair Play have meant that a deal is not possible.