The areas in Scotland where it is now looking for sites include Clarkston, Peebles and Stonehaven.
The supermarket chain currently operates 96 stores in Scotland and more than 900 across the UK.
The retailer stated that the potential new sites should be around 1.5 acres and able to accommodate a 20,000 sq ft 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: “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.”