The Manchester Evening News says United have offered right-back Fosu-Mensah a new contract even though he has started four games in three-and-a-half years for the club.
Various clubs have expressed interest in Fosu-Mensah, 22, and he would be free to negotiate a pre-contract agreement with overseas clubs in January ahead of leaving at the end of the season.
However, manager Ole Gunnar Solskjaer has told the Netherlands international he wants him to stay.
United triggered the one-year extension in Fosu-Mensah's contract last season as they wanted to retain his value due to Fosu-Mensah's positive reputation abroad. Fosu-Mensah switched agents earlier this year and was named in Frank de Boer's provisional Netherlands squad in September.