The controversial forward once more attracted the headlines for all the wrong reasons after appearing to bite Ivanovic midway through the second half of Liverpool's clash with Chelsea.
That the 26-year-old scored a late leveller to ensure the Merseyside club escaped with a 2-2 draw against the Champions League chasers at Anfield is very much an afterthought.
Instead, much of the post-match reaction has centred on his aggression on Ivanovic, with Souness stunned by the incident.
"I'm not sure what to make of it really, embarrassing," he said in his punditry role on Sky Sports 1.
"A football club's board of directors' job is to attract and get the best football players and keep them at the football club.
"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 any Barcelona, Real Madrid, Manchester United, it is up there with any of them."