The Republic of Ireland international has been linked with a switch to Old Trafford since David Moyes quit Goodison Park for Old Trafford in 2013.
Coleman, aged 26, appeared to have slipped on United’s radar when they were rumors that United target Clyne of Southampton is set to join Liverpool.
The report suggests that Coleman, who arrived at Everton from Sligo Rovers in 2008, would command a fee of £20m.
He signed a new contract last year and is now tied to the Toffees until June 2019.
Everton are said to have spoken to Leeds United about Sam Byram’s availability as they prepare for the possibility of losing Coleman, but manager Roberto Martinez would prefer to keep hold of the marauding full-back, But if United makes a good bid the Toffes could be tempted to sell.