The Uruguayan star has been linked with a move away from Anfield in the off-season, and Arsenal have had two bids rejected by Liverpool.
Liverpool reportedly want £50million for Suarez, and Arsenal's latest offer was £10m short of their valuation.
Suarez has insisted his desire to move was due to his treatment in the English press, making La Liga giants Real Madrid his most likely destination.
Rodgers has maintained his desire to keep the 26-year-old, and said a move to Arsenal was a strange choice.
"I know what we are trying to build and grow, so why would you swap Liverpool to go to Arsenal? I am not sure that it adds up, to be honest," Rodgers said.
"Look, Arsenal have a wonderful history in their own right - but Liverpool are one of the biggest clubs in the world.
"We are not in the Champions League and haven't been for a while now, but we have to step up to the challenge now.
"It is difficult for Luis, I understand that. If a team wants you, it can be difficult.
"I am sure Luis will have seen the sheer size and status of the club here, so we'll just see how it goes, but it is not something we want to run on for too long."
Suarez scored 30 goals in all competitions for Liverpool last season, 19 more than the next best - January signing Daniel Sturridge.
Rodgers said he had built his team to suit Suarez, who was banned for 10 matches in April after biting Chelsea defender Branislav Ivanovic.
The Northern Irishman believes Suarez would be making a mistake if he continued trying to force a move.
"He has been given a team built around him. I made some big calls to make it work to suit his strengths," Rodgers said.
"It is no coincidence he had a great season apart from the end bit and we would love to have him to continue the next phase."
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