Rodgers has said he never had any offers for the Brazilian after speculation the midfielder was allowed to leave the club, and gave an injury update on his squad.
Liverpool manager Brendan Rodgers seems to have dismissed any notion that Lucas Leiva was going to leave the club in the summer, or in this January window, by saying he's 'always an important part of the squad'.
Lucas has been down the pecking order when it comes to midfield selection until the past three games when Rodgers has tried to get his side back to basics and winning matches again - where the Brazilian has impressed.
He told his pre-match press conference ahead of this weekend's clash against Sunderland: "We never had any offers for Lucas. He was always an important member of the squad. He's in a good moment and long may it continue."
Rodgers has played Lucas in the defensive midfield role since his return and it looks as though he will stay there in the near future, despite competition for places being intense in that area of the side.
He added that Philippe Coutinho has been struggling with a knee injury but he could be involved with Saturday's meeting against Gus Poyet's side, but Mario Balotelli remains sidelined with a groin problem, meaning Rickie Lambert could make a fifth consecutive start up front.
The Reds' boss said: "He [Balotelli] is injured at moment but he's still very much a Liverpool player. My concentration is on those fit and available.
"Coutinho had a slight issue with his knee, but should be ok for Saturday. [Jose]Enrique has trained and should be ok."
Mamadou Sakho could be in contention for a place in the squad given he was photographed in full training after recovering from a thigh injury.
Another topic for discussion at the moment is Liverpool's goalkeeper Simon Mignolet who made yet another error in the win over Leicester City on Tuesday evening, but Rodgers appears to be behind the Belgian stopper.
"Simon Mignolet is working very hard on the training field to improve."