Mourinho wants a centre-back signed up before the end of the transfer window on 1st September and Roma are considering several names.
Bailly is one of the names on their shortlist but Roma are considering moves for several other players at the moment.
Dan-Axel Zagadou and Japhet Tanganga are two of the defenders the Serie A giants are tracking at this stage of the window.
But according to Italian daily La Repubblica, Bailly is the player Mourinho would prefer to sign before the window closes on 1st September.
The Portuguese signed Bailly when he was the Manchester United manager and remains a firm admirer of the player.
Manchester United are also open to letting him go as he is possibly the fifth-choice centre-back in the squad at the moment.
However, the financials of the deal are a major stumbling block for the Serie A giants at the moment.
Bailly is on a €5m per year contract at Old Trafford and Manchester United also want a significant loan fee if they agree to such a deal.
Fulham, Sevilla, Monaco and Marseille are some other clubs who are interested in snapping up the centre-back this summer.
