The supermarket chain already has branches in Brownsover and Hillmorton - but a spokesperson told the Advertiser they are searching for a site which is 1.5 acres and able to accommodate a 20,000 sq ft store with around 110 parking spaces.
They added that this would ideally be on a prominent main road and with good visibility and access.
The supermarket chain said they would prefer a spot in or near to the town centre - although their space requirements make that sound like a rather ambitious plan.
Ciaran Aldridge, national property director at Aldi UK, said: “We have been investing in Britain for more than 30 years now, but we know that there are still areas that either do not have an Aldi at all, or that need another store to meet customer demand.
“Shoppers are increasingly looking to get unbeatable prices on their weekly shop without compromising on quality.
"That’s why, more so than ever, we’re keen to explore all opportunities to open new stores across the country.”
The full list of locations it is targeting in Warwickshire are:
Shipston on Stour