Suarez has said he wants to leave Liverpool to play in Spain, blaming the British media for making his life impossible in England.
Arsenal have made a £30m bid for the striker, that was turned down, while Real Madrid have also shown interest.
But despite speculation over his future, the 26-year-old has joined up with his team mates in Australia for Wednesday's pre-season match against Melbourne Victory.
Asked whether he expect Suarez to stay, Rodgers said: "Yes, very much so.
"He's a player that obviously is talked about and there's been a been a lot of speculation over the course of the off-season.
"But the reality is that he's a player that's very much valued at Liverpool.
"Unless there's any sort of offer that comes in which is anywhere near his value, then there's nothing to consider - and we haven't had that.
"So at the moment, in this present moment in time, he's back in, he's reported as he should do for training at the right time.
Rodgers added: "I haven't had it yet - we only arrived late last night.
"He was obviously here earlier coming from a different part of the world but as we've always been as a club and certainly as a manager and a coach I'm quite relaxed about it.
"Luis was out here as expected. He's an integral part of our squad. We'll chat at some stage like I do with all the players.
"He'll join training today with all the other players and over the course of these next few weeks we'll all communicate but him and I have been in regular communications throughout the summer."