The Brazilian international has fallen down the Anfield pecking order and wasn’t even part of Liverpool’s squad at the weekend, as Brendan Rodgers saw his side secure a late 1-0 win over Stoke City on the opening weekend of the Premier League season.
The emergence of youngster Emre Can, who can play in a number of roles including as a defensive midfielder, and the signing of James Milner will further restrict Lucas Leiva’s involvement in the Liverpool first-team.
Lucas made 16 Premier League starts last season and was impressive when called upon, but the former Gremio man has spent a large chunk of recent seasons sidelined with injuries and the time may be right for a fresh challenge.
ESPN claim that West Ham are still looking to bring in Cameroon international Alex Song on a permanent deal, having brought in the former Arsenal man on a loan deal last season, but now see Lucas Leiva as a viable alternative.
The Hammers had also been linked to a move for free agent Joey Barton. The 32-year-old is without a club after being released by Queens Park Rangers, and would likely represent a cheaper option than Lucas, although as noted by the BBC on Wednesday, a move is no longer on the cards.
Former Liverpool boss Rafa Benitez signed Lucas in 2008 and the 28-year-old has become something of a fan favourite over the course of the past seven years.
Though his appearances of late have been limited, the enforcer has still amassed 196 Premier League appearances, and that level of experience could be vital for West Ham as they look to push for another top half finish in 2015/16.