The 26-year-old has made no secret of his intention to leave Anfield - publicly voicing admiration for Real Madrid and talking up his delight at being linked with Arsenal, while the north London outfit are preparing a £40 million offer.
But Rodgers says Liverpool will have the final say on a possible departure for Suarez, as he is keen for no player to disrespect the club.
|4/6||Luis Suarez is 4/6 with Paddy Power to score as Liverpool beat Melbourne Victory
"Football and society is different nowadays, the [transfer] market is totally different and players can create different ways to open it up.
"But I have always said that there is no player bigger than Liverpool and that is something we are very strong on.
"Do I expect him to stay? Very much so. A lot has been said in the off season, but the reality is that he is very much a player of importance. Every player has a value and a worth, but it doesn't mean we are going to sell him."
Suarez joined up with the rest of the squad in Australia on Sunday after being afforded an extended break following the Confederations Cup.
Rodgers, who previously revealed that the striker will take part in Wednesday’s pre-season clash with Melbourne Victory, plans on discussing future plans with the former Ajax man during the tour.
"I will do what I have done with the rest of the players and sit down with him," Rodgers said. "The reality is that we do have one or two things to clear up, but that will be done and we will continue to work.
"Luis and I have been in regular contact, but by the time we got here on Sunday night and had a bite to eat, it was late. We have that sort of relationship, though, where communication is open. I always tell him what I feel.
"Luis is here as expected, he is an integral part of squad and we will chat at some stage. The bottom line is he's a Liverpool player. We have only had one bid for him and it was nowhere near the value we have of him and there has been nothing since."