Managing director Ian Ayre flew to Barcelona this week to open preliminary talks about an improved contract for the Uruguay international, who has two and a half years remaining on his current deal.
Suarez wants to play in the Champions League and with the Reds in second place in the table they are in a good position to deliver that this season.
Which is why Rodgers wants the emphasis to remain on the pitch ahead of a tough festive schedule which includes trips to top-four rivals Manchester City and Chelsea.
"There is nothing to report on that," he said when asked about Suarez's contract.
"Contractually, with any players, it is private so at the minute he is just focusing on his football.
"We are just very much focused on our performance level, improving and improving players, and I think that will all take care of itself. I don't think there is any rush at this moment in time.
"Of course he is a player we want to keep here and build the team around in the coming years."
Suarez is the Barclays Premier League's leading scorer with 17 this season, which is even more remarkable considering he missed the first five matches as his 10-game suspension for biting Branislav Ivanovic was carried over from the previous campaign.
On Sunday he won the Football Supporters' Federation player of the year, some achievement considering the abuse he has had from opposition supporters in the wake of the biting incident and prior to that a seven-match ban for racially-abusing Manchester United's Patrice Evra as well as being accused of diving on occasions.
Rodgers believes the 26-year-old has returned a better player and person.
"I think it is part of nature that you mature and the ban hit him really hard last time," he added.
"He is a player every manager in the world would want in his team for his determination and quality.
"But I've got to know him as a human being and I know a lot of things written and said about him couldn't be further from the truth.
"He is a really humble man, he just has this unique desire to win games and we see that week in, week out.
"If you judge him on his football he is up there with the world's best.
"As a human being he's had his difficult moments and we've had our difficult moments with him, but he is a great guy and is really coming to the fore in this period."
Suarez captained the side in Sunday's 5-0 win at Tottenham in the absence of the injured Steven Gerrard and Rodgers believes that is a reflection of his standing within the squad.
"I think it is maturity. He has really felt the love of the supporters because after the 10-game ban he found it difficult to cope," he said.
"He is a man who plays football for the love of the game and we see that every week.
"He is maturing, accepting the role and responsibility I've given him here.
"He is not only a top player, he is one of the pillars of the group.
"We are a young side with an average age (that is) probably the lowest for a number of years and he has taken on that mantle in order to help and support those young players while having that x-factor to his game.
"I just think he is in a good place, his family is in a good place and long may it continue."