The Saints star has enjoyed a fantastic start to the Premier League season, and was recently rewarded with a call-up to Roy Hodgson's England squad for the friendlies against Chile and Germany.
His solo goal against Hull City last weekend demonstrated his ability on the ball, and Southampton's rise up the table has coincided with several of their top stars being linked with January moves.
And the report claims Lallana has now emerged as a potential target for Liverpool, with Brendan Rodgers on the lookout for reinforcements in the attacking midfield position.
The Anfield club were linked with Henrikh Mkhitaryan before the Armenian international moved to Borussia Dortmund and with Willian before the Brazilian joined Chelsea.
Rodgers clearly wants another playmaker to offer competition for Coutinho, and Lallana is believed to be under consideration.
Liverpool have enjoyed a strong start to the Premier League campaign, and with Champions League qualification the aim for Rodgers this term, the Reds boss wants to ensure the club capitalises on their gains so far.
The 4-0 win over Fulham at the weekend means Liverpool sit just two points behind table-toppers Arsenal, and the plan is to carry the momentum through the New Year with new additions in January.