"I was never fortunate enough to play under Bob Paisley, but everyone at Anfield knows what a great manager and a great man he was," said Carragher.
"You only have to look at his record as a manager to realise that he was up there with the best - three European Cups speaks for itself.
"He probably wasn't one for personal accolades, because by all accounts he was very humble, but if there is any possibility of him being knighted then it should happen."
The web address for the petition is http://petitions.pm.gov.uk/SirBobPaisley/