Suarez, who is being chased by Premier League rivals Arsenal, said in a newspaper interview that Rodgers had given his word that the Uruguayan would be sold if Liverpool did not qualify for the Champions League.
"My conversations with players will always remain private. I'll never disclose any conversation between a player and I," Rodgers told a news conference in Oslo after his side's 4-1 friendly victory over Valerenga.
"In terms of the remarks that were made, this is a football club that has always worked a certain way.
"The Liverpool way is all about a club with ambition, a club that strives to be the very best, a club that is about commitment - that means that everyone is committed to the cause of fighting for the shirt.
"It's also about dignity and being dignified in how you speak about the club, on and off the field, it's about unity.
"Those are the four values that run through my mind when I think about Liverpool. Those are the values we will always retain. If anyone steps outside of that standard, I will deal with it. That's something that we'll do."
Suarez's future has been under scrutiny since the end of the season in which he scored 29 goals in all competitions.
Arsenal offered just over 40 million pounds ($62.07 million)for the striker, although Liverpool have maintained that Suarez is not for sale.
Suarez's stand-off with the club has overshadowed an encouraging pre-season for Liverpool, who have won six out of six friendlies, but Rodgers said the striker's situation would not affect the club's preparations.
"There will never be any player or person bigger than the club," Rodgers said.
"Professionally, Luis Suarez has given me everything since I came into the football club, but there is obviously a way in which you have to speak."
Suarez, who did not play in Oslo because of injury, said he might even approach the Premier League.
"Liverpool is a club with a reputation for doing things the right way, I just want them to abide by the promises made last season," Suarez, who is desperate to play in the Champions League, said in the Daily Telegraph.
"I have the club's word and we have the written contract and we are happy to take this to the Premier League for them to decide the case but I do not want it to come to that." ($1 = 0.6445 British pounds)
(Reporting by Martyn Herman, Editing by Nick Mulvenney)
