The Uruguayan has accused the Reds of failing to honour an exit clause in his contract following two rejected bids from Arsenal.
However, Rodgers has branded Suarez's remarks as disrespectful, insisted that no such contract clause exists, and vowed to take action against the player.
"I will take strong, decisive action, absolutely. There has been total disrespect of the club - this is a lack of respect of a club that has given him everything. Absolutely everything," said Rodgers.
"There were no promises made - categorically none - and no promises broken. Obviously, the remarks I've read, it is bitterly disappointing - but my job is bigger than that. My job is to fight and protect the club.
"We have a standard at Liverpool and I will fight for my life to retain it. The Liverpool Way is all about being committed to the cause and fighting for the shirt. It's also about dignity and being dignified in how you speak about the club. It's about unity. If anyone steps outside of those values then I have to deal with it."
Rodgers also hinted that there is a strong possibility that Suarez will not play for the club again unless he makes amends for his behaviour.
"Is there a way back? We first of all need to assess where it's at at this moment things have been said that are derogatory against the football club and his teammates and the supporters," he added.
"There's a few bridges to cross before that can happen [play for Liverpool again]. It's about the respect, that's the only thing we look for. This is one of the most iconic football clubs in the world, you can't disrespect it.
"That's something I will ensure before anything happens in the future. That bridge will need to be crossed."
Suarez will be forced to train on his own following his outburst against the club, according to The Mirror.