The Daily Mirror is reporting that the England international is “on the radar” of the French champions as the January transfer window draws nearer.
The same story says that PSG are keen on a move for Lallana after Edinson Cavani’s move to MLS side LA Galaxy.
Lallana is out of contract in the summer and will therefore be free to negotiate with foreign clubs in the January transfer window.
The 31-year-old has struggled for both form and fitness this season and he has only featured in five of Liverpool FC’s 12 Premier League games so far this season, starting just once.
He scored Liverpool FC’s all-important equaliser in their 1-1 draw with Manchester United at Old Trafford last month but has been limited to a total of just seven appearances this season in all competitions.
According to the same story, Liverpool FC could do a deal for Lallana in January and then put that money towards signing Ryan Fraser from Bournemouth.
Liverpool FC are currently eight points clear at the top of the Premier League table and they will return to action on Saturday with a trip to Crystal Palace.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news