Uruguay international Suarez has two-and-a-half years to run on his current deal but Liverpool are keen to secure his presence at Anfield for an extended period.
Managing director Ian Ayre flew to Barcelona on Wednesday to speak to the player's agent Pere Guardiola about the matter.
But, addressing the media ahead of Liverpool's game with Cardiff on Saturday, Rodgers was keen to stress he remains relaxed about securing a new contract for his star striker.
"There's nothing to report on that. At the moment he is just focusing on his football," said Rodgers.
"That (the contract) will all take care of itself, I don't think there's any rush at this moment in time with anything on that.
"Of course, he is a player we would want to keep here and build a team around over the coming years."
Suarez has been in stunning form since returning to action after completing a 10-match ban for biting Chelsea defender Branislav Ivanovic last season.
The 26-year-old has scored 17 goals in 12 matches, including hat-tricks against West Brom and Norwich.
Suarez previously served an eight-game suspension for racially abusing Manchester United defender Patrice Evra, but Rodgers has defended his player, emphasising he has learned from the punishments.
"It is part of life that you mature. The ban hit him really hard last time," added Rodgers.
"He is a player that any manager in the world would want in the team for his determination and quality.
"But I have got to know him as a human being as well. He is a really humble man who has this unique desire to win games.
"He has had his difficult moments and we have had difficult moments with him, but he is a great guy and he is really coming to the fore in this period.
"He has been outstanding."