Lucas is considering leaving Liverpool after losing his place in the second half of this season, a source told ESPN FC.
The Brazilian had been a regular in the starting 11 when fit since Xabi Alonso moved to Real Madrid in 2009.
But since manager Brendan Rodgers installed captain Steven Gerrard as his first-choice defensive midfielder in January, Lucas has only started four games. Three of those were when an usually ever-present Jordan Henderson was suspended.
The 27-year-old is pessimistic about his chances of reclaiming his spot in the team and was disappointed to lose his place in the Brazil squad.
Lucas, who has won 24 caps and had been part of Luiz Felipe Scolari's plans, was omitted from his 23-man party for the World Cup.
Chelsea's Ramires, Inter Milan's Hernanes, Tottenham's Paulinho, Wolfsburg's Luiz Gustavo and Manchester City's Fernandinho, who are all playing regular first-team football for their respective clubs, were preferred for the central midfield roles.
Lucas joined Liverpool from Gremio for 5 million pounds in 2007 and has gone on to score six goals in 243 games during his seven-year stay on Merseyside, winning the club's player of the year award in 2010-11.
Although he signed for the club as an attacking midfielder, he was converted to a more defensive role by former manager Rafa Benitez.
But the attack-minded Rodgers is only playing with one holding player, leading Lucas, whose last three starts have come on the right of a midfield diamond, to think his future may lie elsewhere.