Bob Peedle, Vice Chairman for Royal Society of St George, said: "It's upsetting when someone in the public eye shows no respect for either Queen or country.
"The England footballer does not show the patriotism that I see from other players.
"I can only assume that he does not know the words to the anthem and is just not prepared to learn them.
"I'd like to see him know the word of God Save The Queen by St George's day and I would be very happy to teach him."
A spokesperson for Wayne Rooney accepted the offer for Wayne to learn the anthem.
He said: "If the Royal Society of St George would like to give us a call we may sort something out."