However, sources at Everton maintain no deal or agreement has been reached.
United are keen to secure the 24-year-old's signature in time to name him in their squad for a pre-season tour of the United States this weekend.
The champions, who have been unable as yet to offload Diego Costa, must now decide whether or not to table their own counter-offer to Everton for Lukaku.
Coupled with the departure of Zlatan Ibrahimovic this summer, Mourinho needed a new striker, and he's got a familiar face in Lukaku after their brief stint together at Chelsea.
Lukaku was a boyhood Chelsea supporter and has designs on returning to west London and proving himself at the club that sold him for £28m three years ago.
The Everton stance appears to be something of a bargaining position, with Lukaku's departure inevitable for several months after he stated his desire to join a club in the Champions League.
In turn, Chelsea could "aggressively challenge" for the player, but "it would now take something significant to dislodge United".
He went on loan to West Bromwich Albion for the 2012-13 season where his goalscoring touch returned as he netted 17 goals in 35 appearances.
Rooney was unable to command a regular starting place in Mourinho's side and started just 15 Premier League games.
It is expected that the frontman will depart the Toffees before the transfer window shut for business on August 31.