A letter sent to neighbouring businesses states it intends to submit a planning application in ‘coming weeks’.
It says it would create 40 full and part-time jobs, have 91 parking spaces, an in-store bakery and toilets and solar panels on the roof.
Sheffield parks: Gypsy’s Brew catering van to leave Bole Hills Park, Crookes
New cafe 'Joni' opening up in Sheffield serving varied range of brunch, lunch and breakfast options
Cole Brothers Sheffield: Grade II listing of former John Lewis slammed as 'ludicrous decision'
Clarks shoe shop relocates as Sheffield's dwindling retail offer shifts to The Moor
Mansfield Road fire station Sheffield: Landmark to become gym, café and climbing wall from January
A plan shows customers would drive in from Eyre Street and leave via South Lane, to the rear of the building.
There is an Aldi supermarket directly opposite on the other side of St Mary’s Gate. But Lidl’s letter states the new store would ‘improve local shopping and customer choice’.
Last year, Lidl announced it was hungry for sites in Sheffield and issued a big list of ‘areas of interest’ which included St Mary’s Gate.
Theatre Deli, which was based in the former Mothercare in the little shopping centre on Eyre Street, was served notice and closed on January 10.
Theatre bosses said the site had been sold by NewRiver – owner of The Moor ‘estate’ – in the autumn.
The Star has contacted Lidl and NewRiver.
Meanwhile, Lidl is set to replace Sports Direct on 50 High Street.
The retailer is set to close in July and and the supermarket take over two floors in the building, which was once House of Fraser.
The firm opened a store in Malin Bridge, Sheffield, last June. Nationally, it has more than 860 shops.