The Uruguayan striker is currently four games into a 10-game suspension for biting the Chelsea defender in their 2-2 draw at Anfield back in April.
The Latics owner claimed that the Reds should have sold the forward due to the controversy.
"I would have sold Suarez, you can't have a player who bites people," Whelan told The Mirror.
"I would never let him pull on the Liverpool shirt again. Do Liverpool really want Suarez wearing their shirt when he bites somebody else?
"Of course, Liverpool will want to get the best fee possible for him, but that was the second time he had bitten someone. If he was a Wigan Athletic player, and he'd bitten somebody, he wouldn't put the shirt on for me again."
Suarez's future has been the subject of intense speculation all summer, with Arsenal having had two bids turned down for the 30-goal striker.
However, the forward has been training on his own as of late after he claimed the Reds had broken a promise to him over a summer move.
Manager Brendan Rodgers recently revealed that the player had to apologise to his teammates before returning to the first team setup.