Horncastle is one of 11 locations across Lincolnshire where the German-based supermarket is hoping to build.
The supermarket chain has been on an expansion drive in recent years as it targets having 1,200 stores open by 2025.
Among the towns it hopes to open in are Horncastle, Mablethorpe, and Market Rasen. It also wants to build additional stores in Cleethorpes, Scunthorpe, and Lincoln.
Aldi, which currently has more than 880 stores across the UK, has identified several new locations in Lincolnshire where it is looking for freehold town-centre or edge-of-centre sites suitable for development.
It says each site should be around 1.5 acres and able to accommodate a 20,000 square feet store with around 100 parking spaces, ideally on a prominent main road and with good visibility and access.
Ciaran Aldridge, National Property Director at Aldi UK, said: “Aldi is growing rapidly and we are welcoming around a million new customers into our stores every year.
“But there are also hundreds of towns across the UK where there is not an Aldi, meaning there are hundreds of thousands of people who can’t easily access the high quality, affordable food our customers love. We are willing to explore all opportunities, including developer-led schemes or existing retail units.”
The full list of locations it is targeting in Lincolnshire are: Barton-upon-Humber, Lincoln, Cleethorpes, Epworth, Mablethorpe, Market Rasen, Scunthorpe, Bourne, Holbeach, Horncastle, and New Boultham (Lincoln).