Bailly, 28, was Mourinho's first signing at Manchester United, joining from Villarreal in 2016 for a fee in the region of £30 million. He played 39 senior games in his first season at Old Trafford. However, recurring injury issues and new signings have put him further down the pecking order.
The Ivory Coast international made just seven appearances in all competitions last season.
He, along with Axel Tuanzebe and Phil Jones, is on the three-man list of defenders who Manchester United are looking to offload this summer.
Bailly could be available for as low as £10 million, but as per Metro's report, Mourinho's side currently want a loan deal.
At Roma, Bailly could also be reunited with former United players Chris Smalling and Nemanja Matic. The former joined Giallorossi in 2019 while Matic joined them this summer.
The Red Devils have signed Lisandro Martinez from Ajax this summer. With Raphael Varane, Harry Maguire and Victor Lindelof also present in the side, Bailly is the fifth-choice centre-back.
Hence, he could look to join the Italian side in search of more playing time under a manager who knows him well. He is set to speak to United boss Erik ten Hag regarding his future at the club and could leave if he's not convinced of getting proper playing time.
Manchester United set to keep forward at the club this summer
According to transfer expert Fabrizio Romano, Ten Hag wants to keep Anthony Martial at Old Trafford this summer.
The Frenchman has had interest from two clubs for a loan deal but the United board have told the player that they want him to stay.
The 26-year-old has been a revelation in the pre-season so far, scoring three goals in four matches.
To put this into perspective, he scored a combined two goals in 23 matches last season for Manchester United and Sevilla.
He joined the Old Trafford outfit in 2015 from AS Monaco for an initial fee of £36 million along with add-ons. He progressed well, showing his potential in the 2019-20 season as he registered 23 goals and 12 assists in 48 matches across all competitions.
However, he fell off the pedal due to injuries and inconsistent form, leading to a loan to Sevilla in January earlier this year. He scored just once for the Spanish side in 12 matches.
However, his recent upsurge in form would've impressed Ten Hag and everyone associated with the Red Devils.