The 26-year-old was heavily linked with the Merseyside club during the summer, after an impressive season in France, where he scored eight goals and made 11 assists to help PSG to the Ligue 1 title.
But, after a transfer failed to materialise, the France international remained at Parc des Princes, and began the 2013/14 campaign under the new stewardship of Laurent Blanc.
However, Menez's future is now shrouded in doubt, following a bust-up with the PSG manager during last night's 3-0 victory over Benfica.
The forward stormed off the bench in the closing stages of Wednesday's Champions League encounter, after Blanc refused to bring him on as a second-half substitute.
And, with Menez now banned from first-team training, Brendan Rodgers is ready to swoop when the transfer window reopens in January, as the Liverpool boss looks to lure the player to Anfield in a cut-price deal.
Arsene Wenger has also been previously credited with an interest in bringing the player to the Emirates Stadium, but with the Gunners now enjoying a wealth of attacking midfield options, it's unlikely that Menez can be accommodated in the first-team.
Manchester United are another old suitor, but that was before the appointment of David Moyes as Sir Alex Ferguson's successor at Old Trafford.
As a result, it's unclear whether the reigning Premier League champions will rival Liverpool or AS Monaco - who are also monitoring Menez's situation - with a bid for the player at the turn of the year.