The firm is to lodge proposals for a new modern food store at Grey Place, six years after failing with a similar plan for a store on the site.
Back then, councillors rejected plans for a food shop, non-food shop and offices at the former Shields car showroom site over concerns the building's design was 'inappropriate', while potential parking problems were also highlighted.
Aldi appealed the council's decision but this also failed when the Scottish Government reporter agreed the development could harm town centre trade for existing retailers.
The firm says the new plans will provide a catalyst for regeneration around the Grey Place site and will bring around 20 new jobs to the town.
A public exhibition about the development is to be held to give local people an opportunity to find out more and to comment on the proposals.
Further details on the venue and timing of the exhibition are still to be confirmed, with the company expected to reveal more about the development's cost and design later this week.
Graham Nicolson, property director for Aldi Stores in Scotland, today said he was excited at the possibility of bringing the brand to Greenock.
Mr Nicolson told the Telegraph said: "We are very excited about our proposals for Greenock town centre, which will provide local shoppers with high quality products at award-winning low prices.
"Aldi is committed to the Scottish food industry, with more than 60 Scottish suppliers bringing the highest quality at excellent value for money across a wide range of products.
"We are looking forward to introducing the Aldi brand to the local community and getting good feedback on our plans for a fresh, modern, local store for the town centre.
"Our development team are currently finalising our proposals and further details will be available over the coming weeks."
News of the proposed development comes just weeks after supermarket giant Asda unveiled bold plans for a £20 million superstore on land off Brougham Street, just along from Grey Place.