They are now consulting with residents before submitting a planning application to Wiltshire Council.
The proposal for the brownfield site includes an Aldi, a replacement garden centre and opportunities for further uses.
It would lead to the creation of up to 40 new jobs for people living in the local area. It would also provide a new access road and associated services to the remainder of the site, which would facilitate redevelopment of the garden centre and land near to the back of the site.
A spokesman for Aldi, said: "We have been keen to open a neighbourhood store in Malmesbury for some time and are pleased to be finally progressing plans for an award-winning Aldi. Many local residents already travel to enjoy the Aldi offer, and opening our doors in Malmesbury would make it even easier for people to shop and save in the local area.
"This multi-million pound investment would provide an enjoyable shopping destination in a high-quality building, and facilitate the provision of employment opportunities on the site.
"Aldi's opening would also create up to 40 new jobs, and we would actively seek to recruit people from the local area to fill these positions."
The site would include around 121 parking spaces with designated parent and child, and blue badge spaces. Landscaping would also be enhanced to provide an appropriate boundary with Crudwell Road.
Residents will be given leaflets outlining the plans and the chance to provide feedback.
But people can also provide feedback on the plans by calling Planning Potential on 01172141820 or emailing firstname.lastname@example.org.