Bailly has just entered his third campaign at Old Trafford, but the 24-year-old has fallen out of favour with manager Jose Mourinho.
The Ivory Coast international has made just five starts in all competitions this season, leading to the possibility of the centre-back being made available for transfer.
According to the Daily Star, Arsenal and Spurs are monitoring the situation ahead of potentially making an offer during the January window.
United are unlikely to be in any rush to accept any bids below their valuation for Bailly, but it may free up a chance for Mourinho to find a proven replacement.
Bailly cost £30m in 2016, while the player has a contract at the North-West giants until 2020.