Topshop took down the Forsyth’s Spire in March 2012 for emergency repairs when engineers discovered it was in danger of collapsing.
But it has still not returned, prompting the launch of a new campaign calling for Green’s Arcadia company to put it back.
Arcadia said it had “no plans” to bring Forsyth’s Spire out of storage. However, the city council warned it could take enforcement action.
The landmark is sitting in a metal yard in Fife as heritage groups in the Capital branded its absence “embarrassing”.
They said Sir Philip – reportedly worth £5 billion – should pay for its reinstatement.
David McLean, a founder of history website Lost Edinburgh, launched a petition calling for the statue’s return and has already collected 1000 names.
He said: “People want to see it reinstated. They feel quite appalled that this rich company hasn’t done anything.
“They’re not a thrift shop. They’ve certainly got the money. It’s a bit of an embarrassment that they seem to have this disregard for Edinburgh’s civic heritage.”
Cockburn Association director Marion Williams said her organisation had filed a formal complaint as long ago as 2013.
She said: “There was no consent for them to take it down, which is a breach, and therefore enforcement should follow. None of us have had success in pursuing it. The disgrace is that the council has let it go.
“Philip Green is worth a few million, so he should pay to put it back. It’s his civic duty.”
A spokeswoman for Arcadia said: “Forsyth’s Spire remains safely in storage with no plans to be reinstated in the immediate future.”
A council spokeswoman said: “Our enforcement team has been in discussions regarding this issue with the owner of the building since the end of 2013. A progress report will be considered by the development management sub-committee in the near future to consider our options.”