Among the areas it hopes to open in Glasgow are Battlefield/Cathcart and Darnley/Pollok as well as Clarkston in East Renfrewshire.
Aldi, which currently has 92 stores in Scotland and more than 880 across the UK, has identified 19 new locations in Scotland 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 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: “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.”