Kop insiders say the Brazilian star could be on his way despite being voted Player of the Year last season.
The Reds have splashed out £49million on midfielders this summer, bringing in Stewart Downing from Aston Villa, Sunderland's Jordan Henderson and Blackpool's Charlie Adam.
That spending spree has created a glut of middle men on Merseyside, with the new boys joining Steven Gerrard, Joe Cole, Raul Meireles, Alberto Aquilani, Christian Poulsen, Maxi Rodriguez, Jonjo Shelvey, Jay Spearing and Milan Jovanovic.
And Lucas, 24, who was signed for £6m by Rafa Benitez in 2007, has made it clear he will not be happy on the bench.
A source said: "Lucas only signed a new deal in March and was voted Player of the Year by the fans.
"But the word is he is leaving and that will shock a lot of people, especially after he played so well last season."
Kop boss Kenny Dalglish is desperately trying to clear the decks to balance the books.
But the Reds have a lot of big names on big bucks.
Fiorentina are keen on flop Aquilani, Anderlecht are chasing Jovanovic and Poulsen has been linked with FC Copenhagen.
But there has been no firm interest in either ex-England star Cole or Argentinian Maxi.