Maggie Nunn, who worked at the store with her former husband John, has written to Standard Aberdeen Investments, the developers of The Moor, calling for the building to be known as Redgates Centre.
Dubbed as the finest toy shop outside London, Redgates closed its doors for the final time 30 years ago and the building was demolished last year.
Development work is continuing to build a H&M clothes store on the Fitzwilliam Gate site and Ms Nunn called for the developers to help keep the memories of the store alive.
She said: “There is so much love and affection for Redgates in Sheffield that it would be great for the new building to be known as The Redgate Centre.
"It would mean an awful lot to the family. There were 52 members of the family involved as shareholders and there were about ten of them who actually worked there so it would be great for them.
"But it would also mean a lot to the people of Sheffield because everyone of a certain age has memories of the shop."
The huge store, across several floors, was a haven of brightly coloured stacks of Lego, dolls’ houses, Subbuteo, Meccano, bikes, outfits, Matchbox cars, railway sets, wooden horses and board games.
And staff would be encouraged to play with toys in the store – especially in the run-up to Christmas each year when it would come into its own.
Ms Nunn added: "Kids could go in and touch and play with toys without the need to buy them. I am doing this for my former husband but also for the people of Sheffield.
“I just think that if we had lots of people behind it then we have more of a chance and I think the timing is right as it looks like they’re just about to start building the store.”
The shop was founded on Fargate by Edwin Redgate in 1857, later moving to The Moor and then Fitzwilliam Gate.
But the building is making way for a new unit for fashion retailer H&M as part of the third phase of the development of The Moor and ongoing development of the city centre.