Reports emerged on Thursday claiming that Everton have accepted a bid of £75million from the Red Devils for the Belgium international, although senior sources on Merseyside insist no agreement has been reached.
Chelsea have been linked with the 24-year-old this summer and United were understood to be focused on trying to sign Real Madrid striker Alvaro Morata.
However, it appears they have now turned their attention to Lukaku but this is likely to just be the start of a lengthy battle.
The Blues allowed Lukaku to leave permanently for Everton in 2014 for £28million and the Toffees are looking to bring in a fee in the region of £90million with plenty of interest in their prized asset.
Antonio Conte reportedly sees Lukaku as the long-term successor to Diego Costa, who could depart this summer, and he has the full backing of owner Roman Abramovich to go out and secure his signature.