The Uruguayan has been linked with a move away from Anfield after a string of controversial incidents, including receiving an eight-game ban for racially abusing Manchester United defender Patrice Evra.
Having arrived in January 2011 in a deal worth around £23 million, the Reds are ready to offer him fresh terms, despite having four years left to run on his current contract.
The 25-year-old is keen to stay on Merseyside, and the club's managing director Ian Ayre is expecting director of football Damian Comolli to open talks with the player's agent over the coming weeks.
"Listen, he's got a contract until 2016, he has said he wants to stay. I am sure Damien [Comolli] will be speaking to his agent," said Ayre.
"Who wouldn't want Luis Suarez? He is absolutely fantastic. He is such a popular member of our team.
"But they are the things we talk about behind closed doors, and we will further that discussion when it is right and proper.
"Luis is a vital and important part of our setup, and long may that continue."
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