Although Suarez's desire to leave Anfield this summer has seemed clear from various interviews he has given over the last few weeks, the Merseyside outfit have emphasised they do not intend to sell the Uruguay international and rejected an offer - understood to be £30 million - for him from Arsenal.
This week Liverpool confirmed Suarez had been named in the 27-man squad for their pre-season tour of Indonesia, Australia and Thailand, saying he was one of three players - all given extended leave due to being involved in last month's Confederations Cup - who would be joining the party "later on in the tour".
And, speaking to reporters at a press conference in Jakarta, Rodgers said: "Luis Suarez is a wonderful player and he is still very much a Liverpool player. No matter who the player is, nobody is bigger than Liverpool Football Club.
"Luis is a very important member of this squad and I am looking forward to working with him again this season after he had such a fantastic season. There has been lots of speculation about Luis moving to another club but, as I said, he is very much a Liverpool player.
"We had an offer that was nowhere near what we value him at. He's one of the top strikers in the world. Of course he wants to work and play at the top level. But unless something drastic happens, he will be staying here."
Last season - Rodgers' first as Liverpool manager, which saw them finish seventh in the Barclays Premier League - Suarez was a major success in front of goal, scoring 30 times.
But the 26-year-old's campaign ended controversially after he was handed a 10-game ban, six matches of which he is still to serve, for biting Chelsea defender Branislav Ivanovic during a fixture at Anfield.
Regarding that incident, Rodgers said: "What Luis did was wrong. He apologised to me and to his team-mates and the supporters. He will serve his punishment and now we have to put it behind us. We will move on and move on together. He knew what he did was wrong and he was told he was wrong by the football club."
The games Liverpool, who flew out from John Lennon Airport on Tuesday, have scheduled for the tour see them take on an Indonesia XI in Jakarta on Saturday, face Melbourne Victory in Australia on July 24 and then play Thailand in Bangkok on July 28.
- Sports & Recreation
- Luis Suarez
- Liverpool Football Club