The Toffees hitman has informed the club that he will not pen a new contract on Merseyside.
His decision will spark a summer bidding war, with Chelsea, Real Madrid and Juventus all chasing the Belgium international.
And The Sun say Jose Mourinho is willing to take advantage of Lukaku’s situation.
“Man United will up their interest in Everton talisman Romelu Lukaku”
They claim the Special One is willing to pay around £60m to land the 23-year-old.
United boss Mourinho sees Lukaku as a long-term replacement for Wayne Rooney and Zlatan Ibrahimovic.
The Sun add that Rooney is expected to leave in the summer and Ibrahimovic – who is yet to agree a contract extension – is undecided on his future.
Mourinho worked with Lukaku during his time at Chelsea.
The striker made just 10 appearences for the Blues during his three-year spell at Stamford Bridge.