Suarez said in a newspaper interview earlier in the week that Liverpool promised him a move to a Champions League club this summer, a claim Rodgers has strongly refuted.
The Uruguayan's words have infuriated Rodgers, who is upset at a perceived lack of respect for the club and, according to a report in the Guardian, the manager will now tell his best player to train separately until he publically apologises.
"There were no promises made – categorically none – and no promises broken," Rodgers said. "The club and his representatives had several conversations and he knew exactly where he was at.
"I think Luis knows the support he's had at the football club and that's something that's been unswerving throughout the whole of last season. Obviously the remarks I've read are bitterly disappointing but my job is bigger than that. My job is to fight and protect the club.
"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. I don't believe there is a clause in his contract that says he can leave for any sort of price."
Rodgers' view was backed up by the PFA on Wednesday, when players' chief Gordon Taylor confirmed he did not think the clause in Suarez's contract bound Liverpool to a transfer should a bid of just over £40 million arrive.
Arsenal have made an offer of £40m plus a pound, which was rejected immediately by Liverpool. The Anfield club are holding out for what they believe to be the player's "correct value" - around £50m.
When asked about the possibility of Suarez pulling on a Liverpool shirt again, Rodgers said: "There's a few bridges to cross before that can happen. 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."
He added that an apology is "something I will ensure before anything happens in the future."
Suarez's future has been under scrutiny since the end of the season in which he scored 29 goals in all competitions.
Suarez's stand-off with the club has overshadowed an encouraging pre-season for the Reds, 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."