Suarez has missed the start of Liverpool's pre-season programme after being given time off following the Confederations Cup, but the Uruguay international's future remains the subject of intense speculation.
Arsenal reportedly failed with a £30million offer for the 26-year-old, who has previously suggested he is prepared to leave Anfield this summer.
However, Rodgers is determined to keep the former Ajax forward at Liverpool and he reiterated that there is no pressure to sell Suarez.
"Yes, very much so," said Rodgers when asked if he expected Suarez to be at the club this season.
"There's been a lot of speculation over the course of the close season but the reality is that he's a player who is very much valued at Liverpool and unless there's any sort of offer that comes in that's anywhere near his value, there's nothing to consider.
"We haven't had that."
Rodgers will continue to discuss the situation with Suarez, but is untroubled by the constant speculation ahead of Wednesday's friendly against Melbourne Victory.
He continued: "As we've always been as a club, I'm quite relaxed about it. He's an integral part of our squad.
"We'll chat at some stage, like I do with all the players.
"But he's back, he's in great spirits. He's obviously an integral part of the group - you could see his closeness with his team-mates last night when they were all seeing him for the first time in a number of weeks.
"He'll join training today with all the other players and over the course of the next few weeks we'll communicate.
"Him and I have been in regular communication throughout the summer."
Asked what that value was, Rodgers replied: "I didn't say we would sell him! I said that every player has a value and a worth. Doesn't mean you've got to sell them."