But Liverpool chief Rick Parry has dismissed the claims and hit the ball back on Tyneside by claiming the Newcastle boss has more chance of picking up his P45 than the Spaniard.
This has ben an on-going spat for some weeks now, that threatens to get out of hand.
Allardyce has a lot of things in his favour, but the fact he was not Newcastle United owner Mike Ashley's first choice as manager, is still touched upon whenever the Magpies lose a match.
Sam wants to be judged after five years, but chairman Chris Mort says he will "review the situation at the end of the season".
Rafa Benitez has already told Big Sam to "put your medals on the table", and we all know the ex-Bolton boss has never won an honour as a player or manager.
Parry said: "I am not necessarily surprised at Sam Allardyce's comments but it's probably best if he focuses on his own issues. We support Rafa wholeheartedly.
Sam's Job More At Risk Than Benitez's!
"We understand Rafa's policies. We don't get swayed from one week to the next. He produces the results It's his judgement that counts."