Wren Kitchens also hope to open a shop at the unit on Westgate Retail Park.
A number of applications have been made to the council in recent weeks regarding the former Toys R Us unit on Ings Road.
A planning application, submitted by chartered surveyors Montagu Evans, proposes a subdivision of the unit, to allow two stores to open on the site.
The plans suggest that Wren Kitchens would open in the larger of the two units, with a showroom on the ground floor and a kitchen planning area on the above mezzanine.
Documents submitted with the application say that the revamped unit could “contribute positively to job creation and economic growth” in the city.
A second application has been made for the erection of signs for Jack’s, Tesco’s new discount chain, in Unit 1B.
There are currently nine Jack’s stores across the country, with the nearest in Barnsley.
Tesco have also applied for a licence to sell alcohol from the new branch.
A Tesco spokesperson said: “We are always looking for potential sites for new Jack’s stores and these applications are part of this process. We will keep the community updated as our plans develop.”
Permission had previously been granted to extend the mezzanine floorspace inside the unit.
A spokesperson for Wren Kitchens said: “Subject to planning permission, Wren Kitchens plans on opening a state-of-the-art showroom at Westgate Retail Park in Wakefield.
“Wren already has eight showrooms across Yorkshire, with a brand new showroom opening in Bradford later this year.
“If permission is approved, Wren will invest in the transformation of the former Toys “R” Us site and will recruit around 20 local people.
“This is part of Wren’s continual expansion of showrooms across the country which showcase the UK’s largest range of kitchens.”
In 2013, Wakefield Council opposed plans for a Tesco superstore, saying it would damage city centre trade.
In a city centre survey last year, we asked readers what stores they wanted to see in Wakefield - and Tesco came second.