The midfielder has been one of the Reds' stand-out performers so far this season, excelling in a deeper central midfield role, and it is thought the club will get in touch with the player's representatives to discuss an extension before the end of the year.
Lallana's current contract is the same which he signed when he joined the club in the summer of 2014, and will have just two years remaining at the end of this season.
The 28-year-old scored his second goal of the campaign with a drilled strike into the top corner as Liverpool thrashed champions Leicester City 4-1 at Anfield on Saturday, impressing as part of a devastating front six.
After just four league games, Lallana has already scored half as many goals as he managed throughout the entire of last season - though it must be noted that he has improved immeasurably since Jürgen Klopp's appointment as manager back in October.
Lallana one of several players in line for new deals
Indeed, Lallana's strike against Leicester was fittingly the 100th goal the club have scored under Klopp, in his 57th game, and the 50th league goal Liverpool have scored in the year 2016 alone.
It was not the only record that the Englishman set on the afternoon, the Reds' No.20 single-handedly covering 13.1km against the Foxes - more distance than any other Premier League player has managed this season.
He broke his own record, having run 12.5km in the previous game away at Tottenham Hotspur, still also significantly more than any other top-flight player.
It therefore comes as little surprise that Klopp would look to tie him down to a new deal, particularly after rumours - albeit likely just paper talk - of interest from clubs such as Spurs in the summer transfer window just gone.
Liverpool are thought to be lining up new deals for a host of new players - with midfielder Emre Can another thought to be in talks - while Dejan Lovren, Divock Origi and Alberto Moreno could also be set for extensions. All four players' current deals expire in 2019.
It is thought that Can and Origi are among the priorities to be tied down, with Klopp keen to ensure the club keep a hold of their most promising young talents for the future.