Morrisons is believed to be behind plans for a major new store on the Cemex office site in the heart of the town.
Although it has not yet officially been confirmed, it is thought the firm is looking to move onto the Evreux Way site, which is currently home to the Cemex House tower block and is due to be redeveloped.
A Morrisons spokesman said: “We are aware that an application has been submitted by a developer and are monitoring the situation.”
Last week the Advertiser revealed that Cemex House and the former Gala Bingo building are to be knocked down to make way for a new supermarket and shops.
Cemex has sold the site and is looking to move to new premises in Rugby.
Robin Richter from town centre management group Rugby First said: “I would have preferred something else because I don’t think we need another supermarket.
“But supermarkets are the only shops doing really well. Others are still in deep recession.”
The new supermarket would have a second floor sales area with ground floor and mezzanine parking underneath, plans submitted to Rugby Borough Council show.
‘Travelators’, lifts and stairs would all be provided to take customers into the store, which would have a pedestrian link with the Clock Towers Shopping Centre.
Morrisons is also opening a store in Corporation Street later this month.
The firm acquired the site from Netto following that chain’s takeover by Asda.
Jenny Haywood has been named as the new store manager.