The Daily Mail says Lallana's current deal at Anfield is due to expire on June 30, while there is a seven-day window beginning on June 23 for Premier League clubs to extend deals for out-of-contract players for the remainder of the delayed season.
While Jurgen Klopp's men are a nailed-on certainty to win the Premier League title this season, it appears Lallana will look for a new challenge having fallen down the pecking order at the Reds.
Klopp is one of Lallana's biggest admirers, describing the midfielder as 'incredible' and a 'pure joy to watch' over a year ago when the player was making a return from injury.
Lallana, who is known to be injury-prone, has managed to stay fit this season but has only made three Premier League appearances for the Merseyside outfit.
In his six seasons at the club, Lallana has made 178 appearances, scoring 22 times and providing 22 assists.