Suggestions of the big-spending Ligue 1 champions making a late move have prompted a flurry of bets, forcing the online bookmakers to slash the odds.
They do, however, see the Spaniard staying at Stamford Bridge as the most likely scenario, going 7/4 for him to leave the Blues.
Sky Bet Football Trader Chris Spicer said: "We saw a sudden flurry of bets on the back of the reports from L'Equipe that PSG were interested having missed out to Arsenal on Mesut Ozil.
"Whether those bets were from informed punters or just followers of the reports remain to be seen, but the French side have no replace Liverpool, who were speculative favourites and are now 10/1."
Odds subject to change.