They are Bradford on Avon, Calne, Devizes, Malmesbury, Marlborough, Royal Wootton Bassett, Salisbury, Swindon and Warminster.
The UK’s fifth largest supermarket chain has been on an expansion drive in recent years as it targets having 1,200 stores open by 2025.
Ciaran Aldridge, Aldi UK’s national property director, 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 company has more than 880 stores across the UK and 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 foot store with around 100 parking spaces, ideally on a prominent main road and with good visibility and access.