Rodgers took charge of the club at the start of June and has made securing the long-term future of the man who has scored 15 goals in 44 Premier League appearances one of his top priorities.
The Liverpool boss is optimistic that Suarez, who joined Liverpool from Ajax in a £22.8 million deal in January 2011, will agree to a new deal.
"I have had a good conversation with Luis over the phone," Rodgers told the club's official website. "From the outset, he has seemed a really good guy. He loves the city and the passion.
"We have exchanged lots of texts. He sent me a text on the first morning, wishing me good luck. He has really bought into what we are trying to do.
"He was really excited about how we played at Swansea last year. He is really keen and looking forward to playing in a similar sort of model.
"There has been good dialogue (on a contract). I would hope going forward that we can close that out."
Rodgers says he is also confident that defenders Martin Skrtel and Daniel Agger will be key players for Liverpool next season. Skrtel was linked with a move to Manchester City earlier in the summer while Agger is believed to be a target for Jose Mourinho at Real Madrid.
"I met Martin for the first time on Saturday and he's a good guy," said Rodgers. "I am looking forward to working with him, likewise Daniel.
"I had a good feeling after I spoke to him. He is very committed to the cause. He has made it very clear that he wants to be here, fighting and working to make the club better.
"These are issues that we will look to find solutions to in the coming months. People always talk about the players coming but what is important are the ones you already have. I look at this group and I see a really good group of players."