The Uruguayan was hit with the sanction for biting Chelsea defender Branislav Ivanovic during a Premier League match, and Graham Bean believes that challenging the decision could result in the suspension being extended.
"The problem they have is the only basis they can appeal on is if it's an excessive penalty," he told talkSPORT.
"That is chaired by an independent chairman and the reality of the situation is that they are walking a tightrope because an appeal panel can actually increase the penalty.
"If I was advising them, I would say to them, 'take it on the chin, put it behind you and move on'. I think it would be a very risky strategy to appeal against it."
Bean went on to say that it was Suarez's "attitude" in the wake of the incident that led to him receiving such a lengthy suspension.
"I think that was probably the wrong attitude to take. He may well have saved himself a couple of games had he just accepted what he was going to be given and moved on," he added.
"The fact he challenged the FA in saying it wasn't worth more than three games, when it clearly was, was a mistake. There was no realistic prospect that he was ever going to be successful in that argument."
Liverpool and Suarez have until midday on Friday to appeal against the severity of the ban.