This leaves Suarez in the last chance saloon - ex-Liverpool star Souness
The Uruguayan striker will face the Football Association after biting the arm of Chelsea defender Branislav Ivanovic at Anfield today and Souness feels he may have given the club no choice than to offload him this summer.
"I'm not sure what to make of it really, embarrassing," Souness told Sky Sports following the match.
"He is making it very difficult for himself to stay at Liverpool, I believe that puts him in the last chance saloon.
"More important than any of that is to safeguard the good name of the football club. This club is a world renowned football club. It is up there with Barcelona, Real Madrid, Manchester United, it is up there with any of them.
"People will be talking about this for a long, long time and it's going to show Liverpool in a very bad light - especially in this week of all weeks, the anniversary of Hillsborough."