The newly capped England international was allowed to leave Old Trafford and join the Clarets on loan in the summer of 2014 by Louis van Gaal. In January 2015, the defender's move to Turf Moor was made permanent.
Keane has developed as a player after improving his game under Sean Dyche's guidance. His form for Burnley has seen him attract interest from the top clubs in the Premier League and the Manchester Evening News reports Jose Mourinho has identified the ex-United man as a transfer target in the summer.
Mourinho replaced Van Gaal at Old Trafford and in his first summer transfer window, the Portuguese tactician urged United executive vice chairman Ed Woodward to bring Paul Pogba back to the club. The France international returned to the Premier League for a world-record fee and the Red Devils boss wants Woodward to help the club in re-signing Keane.
United are preparing a bid of £25m ($32m) in bringing the 24-year-old back to the club. Keane has already expressed his desire to not sign a new contract at Burnley, which has come as an encouragement as Sean Dyche is set to prepare for his star player's exit following the completion of this campaign.
When Mourinho was in charge at Chelsea, he had the services of John Terry in the heart of the back four. The current United manager won three league titles along with other silverware with the Blues captain as the man in the heart of the back four. The former Inter Milan and Real Madrid manager believes Keane can be his 'new John Terry' at United, if he decides to rejoin his former club.
Any move from United will see them face competition from their league rivals. Liverpool and Everton, along with Tottenham Hotspur are also interested in signing Keane. However, the Red Devils remain confident they are in a firm position to bring their former player back to the club.
United inserted a sell-on clause while allowing the central defender to leave the club and a bid of £25m would see Burnley make profit from their star player's sale in the summer.