Therefore, Chelsea are said to be listening to offers of around £40m for the Belgian striker - a huge decrease on the £97m they spent to bring him to Stamford Bridge in 2021.
Lukaku's former club Inter Milan are believed to be the side most likely to move for him after he spent last season on loan at San Siro.
talkSPORT claims that Lukaku has made it clear he has no intention of reporting back for pre-season training despite new manager Mauricio Pochettino being at the helm.
Even though Lukaku endured a largely frustrating season at Inter due to injury and playing second fiddle to Edin Dzeko in the latter stages of the Champions League, that is his preferred destination.
Lukaku still managed 14 goals across all competitions for the Nerazzurri, but that was ultimately a slight mark down on his tally of 15 with Chelsea the season previously.
However, only in his final season at Everton where he notched 25 league goals has Lukaku had a better domestic campaign than his two seasons at Inter between 2019 and 2021.
With Dzeko having now moved on to Fenerbahce, a return for Lukaku should see him receive more game time.
His partnership with Lautaro Martinez proved crucial as Inter ensured Champions League qualification in the midst of their run to the final, with Lukaku being utilised in their Serie A encounters while manager Simone Inzaghi juggled his options to keep players fresh during a busy schedule.
Lukaku is believed to have no interest in a move to Saudi Arabia or Juventus, holding out for a move to Inter to materialise.
BBC Sport claims that Chelsea are looking for around £40m for the 30-year-old, and Inter are expected to go back in with another offer should Andre Onana join Manchester United.
David de Gea's departure from the club makes a deal appear more likely as the Cameroonian has emerged as United's number one target.
Inter are hoping to receive around £50m for their first-choice goalkeeper, money which will then be used to finance a deal for Lukaku.
The Champions League finalists have been linked with Emil Audero, who would be available for a very low fee given Sampdoria's recent relegation to Serie B, allowing them to bring a replacement keeper in while having enough left over to afford Lukaku.