Rodgers says the London club was playing "a wee bit of a game" by bidding £40million plus £1 in the hope of activating a clause in the Uruguay international's contract.
The Anfield club remain adamant Suarez is not for sale and Rodgers said in quotes reported by a number of national newspapers: "I was surprised.
"I've got to say I've always associated Arsenal as a club with class and so there was a wee bit of a game there.
"For us, it's about moving on and doing our own work. There will come a point where they understand our position.
"Obviously they have an interest and they put that interest in with two bids which were nowhere near what the player is worth. That's within their right.
"There is a market in football for players but from us the message is constant: we do not want to sell."
Despite Suarez's chequered disciplinary record, Rodgers insists Liverpool's owners are not seeking to cash-in on their prize asset.
"I'm extremely confident that Luis will be here [next season]," he added. "The offers have come in as you would expect for one of the world's leading strikers but as time goes by I'm gaining more confidence because I have a chance to be with him on a day-to-day basis and he gets the chance to be around his team-mates.
"We're in total control of the situation as a club and that's how it will remain.
"The owners have been brilliant. If it was another club needing the money or desperate for the money it could have been a different story.
"But [owner] John Henry and Tom [Werner, chairman] have been first class through the whole process, so there are no arguments there and it gives you the confidence they are not in any hurry to sell because they understand we are trying to build here."