Jurgen Klopp sarcastically described Dietmar Hamann as "a fantastic source" after the former Liverpool player suggested the club's poor form may lead to a change of manager.
Liverpool head into Wednesday's Champions League group game at Rangers with just four wins to their name from 11 matches this season in all competitions.
Sunday's 3-2 loss to Arsenal leaves Liverpool with 10 Premier League points this term, with that their lowest tally after eight games since the 2012-13 campaign (nine points).
And speaking on Tuesday, Hamann said Liverpool chiefs may soon have to discuss Klopp's future at Anfield after seven years in the job for his German compatriot.
Klopp did not take kindly when asked for a response to Hamann's comments during his pre-match press conference ahead of the Rangers match.
"Who said that? Didi Hamann? Oh great. A fantastic source, well respected everywhere," Klopp said.
"[Being a former Liverpool player] does not give you the right to say what you want, especially when you have no idea.
"I actually think Didi Hamann does not deserve that you use his phrase to ask a question. Do me a favour and ask your own question."
Liverpool have won back-to-back matches in the Champions League, including a 2-0 win over Rangers last week, since going down 4-1 to Napoli in their Group A opener.
That loss to Napoli came in their most recent away match in the competition, though not since September 2019 have they lost successive games on their travels on the continent.
Klopp's mood was not improved after it was confirmed that Luis Diaz will miss the next two months, while Trent Alexander-Arnold and Joel Matip are out for a fortnight.
But the Liverpool manager, whose second-place side sit three points behind Napoli and three ahead of Ajax, insists he is up for the challenge of turning things around.
"If you sleep on a problem, sometimes you realise life goes on. I just stood there at Arsenal and we had lost the game. I knew already that we had three big injuries," he said.
"This is a tough situation but it also a challenge. We always face challenges but we go for it.
"I am sorry to all our people that after last season we go again and it's not the case that we are competing for everything.
"I cannot promise that we will fly [against Rangers] but we will fight, definitely, until someone tells us the fight is over.
"It hasn't got easier since Sunday because of the injuries but the team I saw in training I liked a lot. So let's give it a go."