The England international has been in fine form for the Reds this season with three goals to his name in 11 Premier League appearances.
Lallana is currently sidelined with a groin injury but could boost Liverpool by returning to action in early December.
However, the Reds could be without him permanently from January as PSG are plotting a move to try and lure him to Ligue 1.
Reports claim that they are putting together a £40million bid and are also prepared to treble the wages of the former Southampton man.
The 28-year-old is contracted to the Anfield club until 2019 but after talk of a new deal last term he is yet to enter into discussions over an extension.
Southampton have announced plans for a two-week tour of China as part of their pre-season preparations for the 2018-19 season.