Joe Allen and Jon Flanagan are set to land new deals with Liverpool.
The Mirror says midfielder Allen has enjoyed an extended run in the side and talks have begun between the two parties over an extension to his current contract.
Flanagan, who has missed the entire season after knee surgery, returned to full training last week.
Despite his lack of football, Brendan Rodgers says he is still a big part of his plans for the future, and wants the defender to commit to a new deal, with his current contract set to expire at the end of this season.