Burnley's Michael Keane
Keane has been linked to Everton and Tottenham among others, but wants to go back to Old Trafford.
Jose Mourinho is claimed by The Mirror to be keen, with the centre-back impressive in keeping a clean sheet against them this season.
United have the finances to spend big on Keane this summer, and Burnley are in a tricky spot despite valuing him at £25 million.
Keane's contract expires in 2018 and The Mirror report the defender is willing to let it run down and seal the move he wants on a free transfer next summer if need be.
Burnley's Michael Keane celebrates scoring their first goal
Keane left Old Trafford in 2014 after feeling his path was blocked under Louis van Gaal, only for an injury crisis to later offer chances to players lower down the pecking order like Tyler Blackett and Paddy McNair.
The defender has put that frustration aside and gone onto win a call up to the England squad after a series of impressive performances over the past three seasons.
United showed with Paul Pogba that they are open to re-signing their top talents if situations present themselves and will not be put off by spending big. If they can get Keane for nothing a year later, even better.