The Reds have all but completed a deal for Chelsea forward Daniel Sturridge in January but are still keen on adding further power to their attacking options in the shape of Gameiro, as manager Brendan Rodgers looks to ease the pressure on top scorer Luis Suarez.
Gameiro was one of the most highly sought after French prospects when he joined big-spending PSG in 2011, but has fallen down the pecking order since the arrival of Swedish striker Zlatan Ibrahimovic from AC Milan in the summer.
The 25-year-old French international scored 14 goals in 45 matches in all competitions during his first season at the Parc des Princes, and so far this campaign has five goals in 12 matches.
He would be a versatile option for Liverpool as he is able to play in a variety of forward positions, and it is believed that a host of clubs are monitoring his progress.
Liverpool have enjoyed an overall positive festive period so far with two wins out of three, and they complete the congested run of games tonight at home to Martin O’Neill’s resurgent Sunderland side who are looking to bounce back from their defeat to Spurs.
Rodgers will be keen to bolster his squad in the January transfer window in a bid to elevate his side into European contention in the second half of the season.