The Beatles should appear on the back of the £20 note, according to the boss of the Liverpool Culture Company, Professor Drummond Bone.
The Beatles could be the youngest people to appear on the note
The professor, who is in charge of preparations for the city's European Capital of Culture year in 2008, said the band deserve national recognition.
"They inspired a generation and turned pop into art," he said.
A Bank of England spokeswoman said it was usually only people who had died who were considered.
"We receive lots of suggestions from the public and the decision rests with an ad-hoc committee which is headed up by the governor," she said.
"The general guidelines suggest that the person under consideration should have contributed a lifetime to their field of endeavour.
"Their contribution has to have stood the test of time.
"However, if the Liverpool Culture Company want to write to us with their request, it will certainly be considered."
The musicians would be the first people born in the 20th century, apart from The Queen, to feature on the back of a Bank of England banknote.
The youngest figure to appear on the note to date is Sir Edward Elgar, on the current note, who was born in 1857.
Other figures on UK banknotes include Elizabeth Fry (£5), Charles Darwin (£10), and Sir John Houblon (£50).