The Wales midfielder's current contract is set to expire in the summer of 2017.
Allen, 24, was one of Brendan Rodgers’ first signings after he became Liverpool manager in June 2012, having starred under him for two seasons at Swansea, with the Welsh midfielder making a £15 million move to Anfield two months later.
He has since earned 87 total appearances for the club, recording two goals and three assists in the process, but his performances have often split opinion among the fanbase, with some appreciating his neat passing approach more than others.
Nevertheless, with his current contract set to expire in 2017, Rodgers is said to be eager to tie one of his long-time favourites down to fresh terms and negotiations between the two sides are now claimed to be in progress.
A series of injuries had prevented Allen from stringing together a consistent run of games over the first half of this seasons but, with 19 starts in 24 games across all competitions now under his belt, his showings in recent weeks have served as an encouraging sign moving forward.
After making six consecutive starts in the absence of both Steven Gerrard and Lucas Leiva, a slight hip strain forced him to miss the weekend’s 0-0 FA Cup draw with Blackburn Rovers, although Rodgers expects him to return for Monday night’s trip to former club Swansea.