The Uruguayan forward has three years remaining on his Liverpool contract but is believed to be keen to join a club who can offer him Champions League football.
And Arsenal tested Liverpool's resolve to keep the 26-year-old earlier this week with a bid of £40m + £1, the unusual amount designed to trigger a clause in his contract which means Liverpool have to inform Suarez of the bid.
The forward has just arrived with Liverpool in Thailand as they continue their pre-season tour and Rodgers thinks he should keep faith with his current club.
One of the biggest clubs in the world
"I know what we are trying to build and grow, so why would you swap Liverpool to go to Arsenal?" said the Reds boss. "I am not sure that it adds up, to be honest.
"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.
"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."
The possibility remains that Suarez may try to force through a move but, asked if he thought that would be a mistake, Rodgers replied: "One hundred per cent.
"He has been given a team built around him. I made some big calls to make it work to suit his strengths.
"It is no coincidence that he had a great season, apart from the end bit, and we would love to have him to continue the next phase."