As the new man in charge at Anfield, Rodgers has spent his first few weeks in the job casting an eye over those at his disposal.
He is looking to identify areas which need to be strengthened and those which require key men to be tied down on fresh terms.
Suarez is considered to be integral to the Reds' future plans, with the Uruguay international having become a firm Kop favourite during his 18 months in England.
Rodgers is aware that retaining the South American's services is vital and has already opened discussions regarding a new deal.
He says he has heard enough from Suarez to suggest that the 25-year-old is willing to extend his stay on Merseyside.
"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."