The unsettled 26-year-old is featuring regularly for PSG, albeit in an unfavoured wide position to give way to Zlatan Ibrahimovic, who operates in the middle of the attacking third.
Blues boss Jose Mourinho is looking for that missing piece of the puzzle on his frontline.
Fernando Torres, while making up for his hard work on and off the pitch, is still failing to deliver the goods and the Portuguese manager might be getting impatient and might look to dispose of him this coming summer.
On the other hand, the west London club is anticipated to offer Samuel Eto'o an extension following strings of impressive performances, while Demba Ba is expected to find game-time elsewhere.
Meanhwile, United manager David Moyes is looking to revamp his squad, however, a deal involving Cavani will depend on whether the Red Devils will be able to clinch Champions League qualification or not.
Interestingly, PSG president Nasser El-Khelaifi has handed out a warning to clubs who are looking to snatch any of his players that he will return the favour by buying their team's key superstars.