The Super Eagles captain is yet to make an appearance under Antonio Conte and there are no plans to renew his deal, which expires at the end of this season.
Mourinho, who initially signed Mikel Obi to Chelsea as a fresh-faced 19-year-old, wants to sign the midfielder, so he can give Paul Pogba the freedom to roam.
Ironically, United thought they had landed Mikel Obi 10 years ago and even announced it on their official website, with a picture of the player in their shirt. However, the £4million deal was done directly with the player and his club, bypassing his agents.
The Nigerian midfielder then travelled to London, where he told Sky Sports TV, that he was pressured into signing for the Red Devils and wanted to sign for Chelsea.
The matter was resolved when Chelsea paid United £12m and Lyn £4m.