The centre-back, who was Jose Mourinho’s first signing as Old Trafford boss, has endured a frustrating season after struggling with injuries and form.
According to The Sun, the 24-year-old is ready to leave the club at the end of the season and the Spanish giants have put his name high on their list of potential signings.
Merengues coach Zinedine Zidane was a fan of the player during his time in La Liga with Villarreal before his move to England, and the Ivorian’s name has been put forward to the Frenchman.
Bailly is set to enter the final year of his contract this summer but has been valued at around £35 million despite making just 11 Premier League appearances for the club this season.
Ole Gunnar Solskjaer is looking to bolster his central defensive position during the off-season, and the report suggests that a player-plus-cash deal involving Bailly could be proposed by United in their attempt to land Madrid defender Raphael Varane.
The France international has been heavily linked with a move to Old Trafford, having reportedly told his team-mates that he is ready for a new challenge.