Kokoro has sumbitted planning permission (20/02325/FUL) at a site between Robert Dyas and St Olav Christian Bookshop North Street.
The Korean-Japanese restaurant chain has applied for permission to redecorate the shop front, the shop's intereior as well as installing a kitchen extraction system.
If successful, the site would be Kokoro's 31st restaurant in the UK with other West Sussex sites in Crawley and Horsham.
The building is grade II listed and is believed to have been built during the 17th century.
Part of the heritage statement of the application reads: "It has been found that the propsoed development would sustain the significance of 81 North Street, while introducing a viable and sustainable use to the ground floor of the building.
"The proposals would also restore an active frontage to an important part of the conservation area and enhance the sginificance of nearby listed buildings, which benefit from their experience as a group along North Street.
"Overall, it is considered that the proposed development accords with all local and national planning policy relatiing to conservation of the historic environment."
A determination deadline has been set for November 18.