The Liverpool boss believes the Gunners' unsuccessful attempts to sign the striker have been out of character, but praised the Reds owners for their stance during the saga
Arsene Wenger's side have had two bids rejected for the Uruguayan, who wants a move to a Champions League club.
The second of those was a bid of £40,000,001 in an unsuccessful attempt to trigger a release clause in Suarez's contract, but Rodgers has hit out at Arsenal for undervaluing the striker and their tactical approach to showing interest.
"I have to admit I was surprised by their bid of £40 million and £1... I always associated Arsenal as a club with class," Rodgers told reporters.
"They may be playing a game there, but we will just move on and do our own work, and the message is constant - we do not want to sell.
"There will become a point when they will understand that. They have an interest and put that interest in with two bids that is nowhere near what Luis would be worth. That is within their right, there is a market for players, but our message is constant."
Liverpool are reported to want £55m for Suarez, the same price Paris Saint-Germain paid for Edinson Cavani.
But even meeting that valuation may not be enough, with Rodgers eager to keep Suarez as the start of the Premier League season draws closer.
The Reds boss praised the club's owners' stance during the saga and said he was growing more confident the Uruguay international would stay at Anfield.
"As time goes on I am gaining more confidence that he will stay. We are in total control of the situation and that is how it will remain," he said. "The owners have been brilliant. Maybe if it was another club where they needed the money it could be a different story.
"They have been first class through the whole process and that fills me with confidence that they are in no hurry to sell. They understand that they are trying to build. There has been lots of talk but the board have been very strong.
"There is always a timeline where you would never sell and we are at that stage now because we're so close to the beginning of the season. We are focused on Luis being here, getting in a couple more and ready to be challenging at the top of the table."