The Belgium international wants to quit Old Trafford after falling down the pecking order and has also got Inter Milan and Juventus interested in him.
But United are refusing are budge from their £75million valuation which has opened the door for Napoli to make an enquiry to sign him.
Inter are still the front runners after Lukaku expressed a desire to work with former Chelsea boss Antonio Conte who is now in charge at the San Siro.
United are willing to sell Lukaku but Inter want a two-season-long period with an obligation to buy which is causing the deal to stall.
Nerazzurri are willing to pay £10m for the loan with £60m the follow for the 26-year-old’s signature on a permanent basis.
It was believed Lukaku wanted a deal to be sewn up before jetting off with United to Australia on the club’s pre-season tour.
That looks unlikely, however, and the No 9 has been training this week – something from which he is expected to not boycott in order to force a move.
Agent Federico Pastorello spoke with Inter chiefs this week regarding a move but played down the speed of negotiations.
“It was just a chat,” Pastorello told Sky in Italy.
“I spoke with the director [Giuseppe Marotta] to understand the club’s intentions with the player.
“They will take the decisions, we can’t put a time frame on it.
“What is clear is that if Inter want the player, they will need to get a move on. Inter are seriously trying to sign him, they are all out for him.
“Goals are not always there to be reached, but it’s a declared target. At the moment, it remains a complicated dream.”
Lukaku has scored 42 goals in 96 games for United since signing for £75m in July 2017.
Speaking about a prospective move to Italy in April, Lukaku told Sky Italia’s Lords of Football: “Playing in Serie A is a dream, it would be really a dream.
“I hope to be able to play sooner or later, even if at the moment I am focused on the United.”