According to ESPN FC, Lucas Leiva will be allowed to leave Liverpool after falling out of favour with manager Brendan Rodgers.
Lucas did not travel with the squad to Stoke for Liverpool's 1-0 win in the opening match of the Premier League season on Sunday and it is suggested his playing time will be severely limited if he opts to stay at the club.
The Brazilian made 20 league appearances for the club throughout the previous campaign; completing an impressive 87% of his total attempted passes, while weighing in with four defensive actions per match.
Nonetheless, he has effectively been demoted to fifth place in the Reds' pecking order, with captain Jordan Henderson, new signing James Milner, youngster Emre Can and Welsh international Joe Allen all ahead of him in the contest for selection.
For West Ham, the Brazilian would represent a viable alternative to Alex Song, for whom - due to his current injury - the Hammers have been unable to secure a permanent move following a hugely successful loan spell last season.
The club hierarchy are monitoring Lucas' situation at Liverpool and are weighing up a move for the 28-year-old, should they decide not to pursue their interest in the Barcelona midfielder and Cameroonian international.