The Portuguese manager is heavily expected to take the reins at Old Trafford shortly and has already jotted up a summer shopping list of players.
The Red Devils have had problems in that position since Gary Neville retired, with the likes of Rafael, Antonio Valencia and Matteo Darmian all trying to fill that void in recent years.
It is a position which worries Mourinho and, according to Sport, the former Chelsea boss will try to lure the 27-year-old from Goodison Park this summer.
If rumours are to be believed, Mourinho also wants Coleman's Everton team-mate John Stones to line up in central defence for him next term (The Guardian), having tried and failed to sign him for Chelsea last summer.
The Toffees are said to have rejected a £37 million bid for the 21-year-old last summer, meaning it may take more than that for the 53-year-old to get his man this time.
That being said, Everton are yet to replace sacked manager Roberto Martinez, but the Spaniard's successor may not be willing to lose two of the team's back four.
Former Chelsea manager Jose Mourinho leaves his house in London