The 20-year-old looks set for a loan spell in the German top flight, with the Daily Mail reporting the two clubs have already engaged in talks.
Chong was given a rare cameo in United's 2-1 win over LASK in the UEFA Europa League on Thursday night, taking his total to just nine appearances this season.
The report adds that a loan fee and wages still need to be finalised before the move is completed.
"That we are in exchange is the case. We are in good talks," Bremen sporting director Frank Baumann said, as per the Sun.
"Several parties are involved. Some things still have to be clarified and we have to agree. As of now, this is not the case."
Meanwhile, former United midfielder Angel Gomes officially joined Ligue 1 outfit LOSC Lille on a free transfer but he will spend the season on loan at Portuguese outfit Boavista.