The Gunners put in a bid of £40,000,001 for the striker earlier this week but Rodgers argues that it will take a lot more than that before the Uruguay international is allowed to leave Anfield.
"If Arsenal want the player, then they have to produce the value for the player," Rodgers told reporters in Australia.
"There was an offer a few weeks ago of £35million and two weeks later it is now £40m and a pound - I don't think it is anywhere near the value of what he is worth.
"But it is twofold, really. A player may want to go, but then somebody has to pay the value or worth of that player."
Suarez featured briefly as a substitute for Liverpool in their 2-0 victory over Melbourne Victory on Wednesday and the Reds boss expects the striker to play for as long as he is paid by the club.
Rodgers added: "There is no change for me or Luis. He is a paid player at Liverpool so he just needs to get on with getting fit. That is how it is.
"Until somebody tells me something different, that is what all my concentration will be on. There will be no games played at Liverpool.
"Luis is part of the group and he knows the standard you have to meet at this club - on and off the field.
"After the bid came in Luis was OK, he said he was OK to go on the pitch and his focus was fine.
"It may be a distraction but players are played enough money now to produce for their clubs and he just has to keep his professionalism, which he has done."