The 28-year-old has made seven appearances for Man United last season, with just four of those outings coming in the English top flight.
According to Sky Sports News, Fulham have approached the Red Devils to discuss a potential loan deal for the centre-back.
However, it is understood that the Ivory Coast international is not currently interested in leaving Old Trafford and wants to fight for the regular spot during the upcoming season.
Bailly still has two years remaining on his contract at Old Trafford, with the option of a further 12 months.
He has made 113 appearances for the Mancunian giants since arriving from Villarreal in July 2016, scoring once in the process.
The Cottagers are back in the English top flight for the 2022-23 campaign, having won the Championship title last season.