The 25-year-old has fallen down the first-team pecking order at Parc des Princes this season, following the summer arrivals of Ezequiel Lavezzi and Lucas Moura.
Carlo Ancelotti has favoured the South American duo in his starting XI for much of the campaign, and with increased competition for places in the French capital, Menez has seen his action limited.
Reds boss Brendan Rodgers is hoping to take advantage of the France international's current predicament, by offering him an escape-route to Anfield.
A £6million bid should be enough to tempt PSG into selling Menez to Liverpool, with his current contract set to expire in 2014, he is unlikely to pen a new deal with the Ligue 1 leaders if his situation doesn't change.
Last week, his agent, Jean-Pierre Bernes, told France Football that Menez is "a competitor who won't put up with being relegated to the bench for much longer".
Liverpool could face competition for the player's signature, though, with Juventus ready to make a bid. However, the Serie 'A' giants are by no means favourites to land Menez, after the playmaker endured a troubled spell in Italy during his time with AS Roma.