Goal has learned that Reds managing director Ian Ayre has begun discussions with the in-form forward's agent, Pere Guardiola, with a view to tying their star player down to a new deal worth more than £130,000 [€156,000] per week.
Though he insists that discussions are "private", Rodgers is calm about the prospect of being able to "build a team around" the Uruguayan in the coming seasons.
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"I think it will all take care of itself. There's no rush at this moment in time, he's a player we want to keep here and build a team around in the next couple of years."
Rodgers praised the attitude shown by Suarez, who had been pushing to leave Anfield before the start of this season, on and off the pitch this season.
"He is maturing, accepting the role and responsibility I've given him at the club," the Northern Irishman said of the forward, who captained his side against Tottenham on Sunday. "He is one of the pillars of the group, for me.
"He's in a good place and long may it continue. He is a humble man with a unique desire to win games.
"If you judge him on his football, he is up there with the world's best."