Lukaku has been linked with a move away since returning to the Blues from Inter Milan last year, and the London club is said to have offered him to other clubs.
According to But PSG, the French giants are considering bringing the Belgian international to the Parc des Princes, as speculation about Kylian Mbappe's departure grows.
The 23-year-current old's contract expires in the summer, and because he has not agreed to a new deal, he is free to speak to other clubs, with a move to Real Madrid heavily tipped and Les Parisiens set to seek a replacement should the Frenchman depart.
Following his £100 million return to Stamford Bridge in the summer, Lukaku was quick to praise former club Inter Milan, causing a reported rift with manager Thomas Tuchel.
Due to this squabble, the striker has only made 12 Premier League starts this season, totaling 36 appearances in which he has netted 12 goals after scoring 64 times in 95 games for the current Italian champions.