Lidl has said they are planning to build the store on Peterborough Road on the edge of the town.
However, Aldi have said if the Lidl store is not built, they would build a shop at the Deepings Centre.
Both Aldi and Lidl have said their stores would create around 40 jobs.
Lidl put a plea out to find suitable land to build a new store in Deeping in 2021, before settling on the Peterborough Road location.
Traders in the town centre have objected to the Lidl store, saying it would cause a negative impact on their businesses – and have instead said the Aldi plans would increase footfall for all firms.
In an open letter to the members of South Kesteven District Council Planning Committee, the 18 traders said ‘we need your help to protect the town centre and the businesses that provide for the local community as our businesses recover from the Covid-19 pandemic.’
They added: “An out-of-town Lidl supermarket would harm our livelihoods. It would draw footfall away from the
town centre. It would decrease passing trade to the town’s many small businesses.
"One of the considerations that planning policy allows when considering out-of-town retail is the impact that it would have on the high street. Policy DEP2 in the council’s Local Plan specifically says that “out of centre locations will only be considered if sequentially preferable sites are not available.”
“A town centre site is available for an equivalent store at the Deepings Centre. The owner of the Deeping Centre has said that they could develop the site, and Aldi have announced that they would build a new store there. This would support town centre businesses, as people would link trips to other shops, pubs, cafes, and restaurants when they visit Aldi for groceries.
"Market Deeping welcomes a new discount food store, particularly as people try to manage the rising cost of living. But we can have either an Aldi that will support the town centre, or an out of town Lidl that would harm it.
"As members of the planning committee, the decision is down to you. Please make the choice to support our high street.”
The letter was signed by Animates Vets, Riverside Beads and Crafts, Chester’s Tearooms, The Cigar Shop, Deeping TV, The Little Sewing Shop, Fillers Sandwich Bar, The Stage, Godsey Lane Coffee, Willow and Grace Bridal, Iron Horse Ranch House, Penny at Callows Barber Shop, Pets Pantry, Linford’s Fish and Chip Shop, Private Kollection, Manna Flowers, Ooh la la Beauty and The Deeping Centre.
The council’s planning committee will meet on Thursday, May 19 to discuss the Lidl plans.