The 40-year-old says the offer of £40m plus £1 for the Uruguay international was "derisory" and admits he was forced to be tough on the striker following his comments in the summer
Arsene Wenger’s side had prioritised the signing of the Uruguay international during the summer transfer window and believed they had triggered a release clause in the striker’s contract when they submitted an offer in excess of £40m.
Rodgers insists Arsenal stood no chance of prising the 26-year-old away from Anfield and labelled the club’s bid as “derogatory”.
“To be honest, we laughed. We were away at the time on the pre-season tour when I saw the bid in writing,” Rodgers told reporters.
“I think Arsenal were ill-advised on that, to say the least.
"Arsenal as a football club always had great integrity historically and so, when that bid came through, I can only say it was one of the worst pieces of information they ever received.
"It was never going to succeed. At the time we certainly saw the bid as derogatory. The two clubs have historically had class, it has been the hallmark of both, but whether it was £40m and one pound or £40m and one penny, our fight was always to keep him here because he is a top player."
Suarez was ordered to train alone in August after the striker claimed the club had broke their promise of allowing him a move away from Anfield if Champions League football was not secured.
"I'm sure all the players are looking to the manager in a situation like that to see what happens," said Rodgers.
"It cannot fester and be allowed to become a cancer within the group.
"No matter how difficult the situation was, we were leading up to our first game of the season having had a brilliant pre-season and nothing could be allowed to stand in the way of our preparation for that.
“My job is to protect the club and it was important during that time that the power of the club was seen."