The Italian side have been credited with an interest in signing the Belgian forward this summer as they bid to strengthen their attacking line-up.
Lukaku’s situation at Old Trafford has been a source of speculation this summer after he fell down the pecking order at the club in the second half of last season under Ole Gunnar Solskjaer.
The 26-year-old Lukaku scored 12 goals in 32 games for Manchester United last season as the Red Devils finished in sixth place in the table.
Inter Milan are thought to be keen to bring the former Chelsea FC striker to the San Siro this summer, but Sky Sports News reporter Solhekol has now suggested that it may be time for the Serie A side to move on after their bid was rejected.
Solhekol wrote on Twitter: “Manchester United have rejected £54m bid from Inter Milan for Romelu Lukaku. Time for Inter to move on. They’re trying to buy something they can’t afford.”
Manchester United finished sixth and without a trophy last season after sacking Jose Mourinho and replacing him with Solskjaer.
The Red Devils have signed two players so far this summer, after wrapping up deals for Daniel James and Aaron Wan-Bissaka.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news