The Premier League transfer window closed on Thursday, so Liverpool face an anxious wait to see if Barcelona make a swoop for Rabiot before the Spanish window shuts on August 31.
Rabiot has so far refused to sign a new contract and would be available on a free transfer next summer if he does not come to an agreement with PSG before then, while Liverpool would be free to discuss a pre-contract deal from January.
"It's not certain if Adrien stays at PSG. It all depends on him," PSG boss Thomas Tuchel told reporters following the Sunday's opening-day win.
"For me he's a great player He can grow even more and become a top player."
Rabiot has made over 200 appearances for PSG since his debut in 2012, scoring 22 goals in all competitions.