The 20-year-old spent last season at fellow Premier League side Crystal Palace, making a total of 21 appearances in the top flight.
Fosu-Mensah was also part of Jose Mourinho's squad for this summer's tour of the United States and the friendly defeat to Bayern Munich on Sunday.
However, the Netherlands international is believed to be seeking another temporary spell away from Old Trafford due to a perceived lack of first-team opportunities at present.
According to Sky Sports News, the Cottagers are hoping to push through a late loan move for Fosu-Mensah in order to bolster their squad ahead of their return to top-flight action.
Fosu-Mensah, who has made 21 senior appearances for United since making his debut under Louis van Gaal in 2016, has also been linked with a temporary switch to German side Hertha Berlin.