The 29-year-old is back at Old Trafford this summer following a loan spell at Marseille during the 2022-23 campaign, but he is not in the plans of Red Devils head coach Erik ten Hag moving forward.
There has been a host of speculation surrounding the defender's future during the summer market, with Fulham thought to be interested, while Al-Nassr and Al Ettifaq have also been linked with a move.
According to the Daily Mail, two Saudi Pro League clubs have officially made offers for the Ivory Coast international, although the size of the bids are unclear.
Sky Sports News reporter Dharmesh Sheth recently said that Bailly had been offered a three-year deal worth £20m by an unnamed Saudi Arabian outfit.
The Ivory Coast international's contract with the Red Devils is due to expire next June, although the club do have the option of activating an additional 12 months.
Bailly make the move to Old Trafford from Villarreal in 2016, and he enjoyed a productive first season at Old Trafford, making 38 appearances in all competitions.
However, the centre-back has struggled with a number of fitness issues since then, failing to make more than 13 Premier League appearances in a single season since 2016-17.
Bailly only made seven appearances during the 2021-22 campaign, which led to him moving to French giants Marseille last summer.
The Ivorian made 23 appearances for the French outfit, who turned down the chance to sign him on a permanent basis.
There have already been centre-back departures at Old Trafford this summer, with Axel Tuanzebe and Phil Jones both being released, while Harry Maguire's future is also being called into question.
Jonny Evans remains with the club, though, and there have been strong rumours that the Northern Ireland international could be handed a one-year contract at Old Trafford.
Man United will round off their preparations for the 2023-24 campaign with friendlies against Lens and Athletic Bilbao this weekend, but Bailly is not expected to be involved in either match.