Lukaku, who rejoined the Blues for a club-record £97.5million from Inter Milan in the summer, hit the headlines in recent weeks for voicing his frustration with his situation at Stamford Bridge in an explosive interview.
He apologised to fans in a directly on social media and has since featured twice for the Blues, scoring in the 5-1 victory over Chesterfield on Sunday.
The 28-year-old must still win over the fans and firing a glut of goals will go a long way to redemption.
However, according to Catalan outlet El Nacional, Roman Abramovich is considering selling Lukaku as he's still disappointed with how his record signing expressed his unhappiness at the club.
The report suggests PSG are ready to tempt the striker to Paris with an offer of £75.5m as they look to replace Mbappe.
The 22-year-old is widely expected to join Real Madrid on a free transfer at the end of the season, with Los Blancos failing in a huge £171m bid last summer.
PSG naturally need a striker to replace him in the XI and Lukaku may well be open to another transfer - especially after he said he was promised a different role under Thomas Tuchel at Chelsea.
Lukaku has scored 198 goals in 410 league appearances since making his debut for Belgian outfit Anderlecht in May 2009.
He has eight goals in 20 appearances for Chelsea this season, having missed a fair chunk of the campaign with injury.