The 31-year-old is not expected to be part of Enzo Maresca's plans at Stamford Bridge during the 2024-25 term, with the former Leicester City head coach planning to implement a specific style of football in West London.
Consequently, Lukaku is highly likely to make a permanent departure from Chelsea this summer, after spending last campaign on loan at Roma in Italy.
The Belgium international enjoyed a steady campaign under the stewardship of Jose Mourinho and then Daniele de Rossi, netting 13 times in 32 Serie A contests.
One of the remaining lights of a golden generation for the Red Devils, Lukaku is currently away at Euro 2024 for Belgium in Germany, where Domenico Tedesco's troops are fighting for continental glory.
Chelsea 'reveal' asking price for Lukaku
According to Italian journalist Gianluca Di Marzio, Chelsea have revealed their asking price for Lukaku as they seek to offload the attacker for good this summer.
The report claims that the Blues value the former Manchester United poacher at €40m (£33.9m), with a number of top European clubs monitoring the player's situation at Stamford Bridge.
It is believed that Maresca's men are not currently willing to dip lower than their asking price of Lukaku, who is fully expecting a transfer prior to the start of the new term.
Leading the race to sign the 118-time international in Italy, AC Milan and Napoli are both keen on securing the services of the ex-West Bromwich Albion loanee.
Contact between the Rossoneri and Chelsea has supposedly been made, however a formal offer is yet to be submitted by either of the Italian duo.
Napoli's Lukaku deal has moving parts
Although Napoli's interest in Lukaku is genuine, it is highly likely that a major outgoing will need to occur in Naples before the 2023 Serie A champions launch a serious pursuit of the Chelsea striker.
The obvious candidate to move on this summer is talisman and leading markman Victor Osimhen, who has been extensively linked to Arsenal, Chelsea and Paris Saint-Germain in recent weeks.
A move to the French capital appeared most probable at first for the Nigeria international, however talks between the Ligue 1 champions and Napoli have since stalled.
Whilst a transfer saga brews, Lukaku will be hoping to fire Belgium to the last eight of Euro 2024 with a win over France on Monday afternoon in Dusseldorf.