Lambert signed from Southampton last summer but hasn't been able to make much of an impact.
Lambert signed for the Reds last summer from Southampton for around £4.5 million but struggled to get regular game time last season, managing to score just the three goals in all competitions.
The 33-year-old was subject to a bid from Aston Villa last winter, and has been linked with a move to other Premier League clubs so far this summer.
It comes as Liverpool have added Danny Ings to their ranks, and persistent reports suggesting Brendan Rodgers is looking to add another striker to his ranks, with Villa's Christian Benteke strongly linked.
There are also reports that Lambert, along with fellow strikers Mario Balotelli and Fabio Borini will be part of a clear-out this summer as Liverpool look to improve on last season's disappointing campaign - where the strikers struggled as a whole, leaving the side scoring 49 fewer Premier League goals than the season before.
For much of last season, Lambert was left on the bench and never really had a run of games in the side he would've liked.
There was a period between November and December where Lambert was starting on a semi-regular basis, and a couple of games towards the end of the season. As a result, Liverpool probably haven't really seen the best of him.