Arsenal are the frontrunners as Cavani would prefer to move to London over Manchester, with Manchester United also thought to be interested should they decide against making Radamel Falcao's move permanent.
But PSG will only let Cavani leave the Parc des Princes should they land their first choice target to replace him - Real Madrid's French international Karim Benzema.
As reported by Spanish journalist Manuel Esteban, Benzema could be the odd man out at the Bernabeu at the end of the season.
"Benzema is on thin ice," Esteban told La Goleada. "If they receive a big offer, they will not be hesitant."
Liverpool had hoped to make Benzema their big money addition, preferably in January, as their season is in danger of becoming a catastrophe. Summer signing Mario Balotelli has proved to be a flop so far, and Danny Sturridge has struggled with injury.
As a result, the Reds have been forced to lean on Rickie Lambert, and they're already out of the Champions League and in danger of missing the top four and qualification for next year's competition.
Should PSG sign Benzema, and the Frenchman may be open to returning to his homeland should Real Madrid force him out, that would end Liverpool's chances and boost Arsenal's hopes of signing Cavani - who surely would not be kept on in Paris with Zlatan Ibrahimovic the club's undisputed number one forward.