The in-form Uruguay international is the Premier League's top scorer with 17 goals from only 11 appearances and reports have claimed managing director Ian Ayre had spoken to the player's agent, Pere Guardiola, to open talks about a new deal.
Liverpool boss Rodgers was coy when asked if the Merseyside club have entered negotiations with a view to extending the former Ajax man's stay at the club.
"There's nothing to report on that (Suarez contract)," he said. "Contractually, with any players, it is private so at the minute he is just focusing on his football.
"We're just concentrating on the football, on performance levels and improving.
"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 was also quick to praise the attitude shown by Suarez, who looked set to leave Anfield before the start of this season, on and off the pitch this season.
"He is maturing, accepting role and responsibility I've given him at the club, he is one of the pillars of the group for me," he added.
"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 world's best."
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