Controversy struck during the second half of Tuesday's World Cup Group D decider, as Suarez appeared to bite Chiellini as both players jostled for possession of the ball shortly before Uruguay's winning goal.
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He told Goal: "Suarez should be banned for what he did. You simply can't do that and expect to get away with it. I feel for Liverpool and Brendan Rodgers in particular who stood by him after he was given a 10-match ban for biting Chelsea's Branislav Ivanovic.
"The club was under a lot of pressure to sell him but they gave him another chance and he rewarded them with some brilliant performances last season. I don’t know if the football authorities will want to make an example of him after this latest incident and extend any ban to cover all forms of football. I hope that is not the case because Liverpool don't deserve that."
Record appearance holder for Liverpool, Callaghan, meanwhile, is also hoping that Suarez's actions will not affect the Reds, where a ban extending to the Premier League could potentially see him miss a large chunk of the 2014-15 campaign, if not more.
"It doesn't look good for Suarez and I fear the worst for him," Callaghan told Goal. "He is a phenomenal player but there is clearly something in his makeup that makes him do stupid things. I played professional football for 20 years and never saw a player bite another, but he's done it three times now, I don't understand it.
"I'm not sure of the rules but any ban should be for his country first and last. It should not impact on Liverpool who got him to behave impeccably when he returned from his ban last season. He scooped all the player of the year awards and although he won it because of his goals, part of the reason was that he had seemed to sort his head out.
"I'm sure everyone at Liverpool will stand by him because of what he has achieved for the club but no one at Liverpool will condone behavior like this. It is unforgivable even if you are a player out of this world."