Supporters want to honour the member of the team's Famous Five players of the 1940s and 1950s with the tribute at a new housing development close to Easter Road.
However, Edinburgh City Council officials say the move is impossible because rules insist streets cannot be named after someone until at least ten years after their death.
Local councillor Alex Lunn has now launched a campaign to get the honour for the striker, who died last year aged 84. Cllr Lunn said: "Lawrie Reilly is a Scottish football great. Naming a street next to his stomping ground of Easter Road Stadium after him is the correct thing to do."
A council spokeswoman said: "It is council policy that streets are not named after individuals who are living or recently deceased. Names can however be added to the appropriate street name bank to be held and used after a suitable length of time has passed."
However, these rules do not apply in other regions, as shown when Fife Council named a new housing development Ian Rankin Court in honour of the author's Cardenden birthplace.