Talking on Sky Sports News, Redknapp described the incident as "indefensible" and "an incredible act of brutality".
Meanwhile, Souness added: "I'm not sure what to make of it. Embarrassing. He's making it very difficult for himself to stay at Liverpool, that puts him in the last chance saloon.
"Most important is safeguarding the good name of the football club. Liverpool are world renowned. People will be talking about this for a long, long time, and it will show Liverpool in a very bad light. This is not the first time he has bitten someone in the football match.
"He is risking everything this great club stands for. I've never seen something like that in a football match before. There are lines you just can't cross, and he has crossed it today. Those pictures will be beamed across the world. It's very difficult for Brendan Rodgers to defend him. We will get politicians involved in this and everything."
Suarez was banned for a similar incident while he was playing for Ajax back in 2010.