The Gunners lodged a £42 million bid for the Uruguyan on Monday and Goal understands that the 26-year-old is preparing to hand in a transfer request to force an exit from Anfield.
But Rodgers feels that Liverpool's superior stature in the game would mean that a move to the Emirates Stadium is illogical, especially after Suarez received a standing ovation from a sold-out 95,000-capacity MCG on Wednesday.
"Would it be a mistake for Luis to leave Liverpool? Yes, 100 per cent," the Reds boss told reporters. "I know what we are trying to build and grow here, so why would you swap Liverpool to go to Arsenal? I am not sure that it adds up, to be honest.
|SUAREZ TO HOLD ARSENAL TALKS
|6/4||Luis Suarez is 6/4 with Coral to stay at Liverpool this summer
Rodgers, however, notes that the lure of the Champions League could play a part in Suarez's desire to leave Liverpool - with the club absent from Europe's elite competition since 2009-10.
But the manager is keen for the club to grow with the striker and feels that his guidance can see the Uruguayan continue his prolific form from last season at Anfield.
"We are not in the Champions League and haven't been for a while now but we have to step up to the challenge," he continued, "and we would love to have [Suarez] to continue with the next phase.
"It is something to be given a team that is built around you. I made some big calls last year to make it work to suit his strengths and it is no coincidence he had a great season apart from the end bit.
"It is difficult for Luis, I understand that. If a team wants you, it can be difficult but it is a situation we are in control of because he has three years left on his contract. Unless something changes, or there is an offer which is heavily increased, he is still very much a Liverpool player.
"And I can categorically say that the owners have been brilliant throughout this process. The board and club has stayed very strong. It is very simple. We don’t want to sell one of our best players."
Meanwhile, Glen Johnson echoed Rodgers's sentiments and feels that the club are moving in the right direction under the Ulsterman.
"You wouldn't walk away from this club easily," the full-back remarked to the Liverpool Echo. "We are building under Brendan. With the owners that we have now, you can see the foundations are there and everything is going the right way.
"If we can keep the players that we have got here, then everything looks promising. The members of staff, the players - we are all the same. We want to keep him here."