Arsenal have upped their bid to £40,000,001 to sign the Uruguayan, but Liverpool's managing director Ian Ayre reaffirmed that both offers made by the Gunners have been rejected and the club's stance has not changed.
"It's never been our intention to sell Luis," said Ayre. "We've received two separate offers from Arsenal and rejected both."
Arsenal are the only team to have formalised their interest in Suarez, while reports suggest that Real Madrid, the preferred destination for the 26-year-old, are unlikely to make a move for him.
Rodgers, speaking at a press conference during the Far East tour, questioned whether Arsenal represented a big enough step up for Suarez to justify him leaving.
"I know what we are trying to build and grow, so why would you swap Liverpool to go to Arsenal?" Rodgers said. "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."