The former Rasa Plus convenience store in Dereham Road could become a kebab shop if the scheme is approved.
The applicant, Makwan Nader, says if his proposal would “add to the mix” of takeaways and restaurants already on Dereham Road.
According to the plans, Dubai Shawarma will serve a range of kebabs, including doner and shish, as well as rice, salads and fries.
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There are no plans for a delivery service from the site, which proposes opening between 11am and 9pm, seven days a week.
The business would join Dereham Road Chippy and Turkish restaurants Antep Kitchen and Mr Mangal.
As the shop is near a large Co-op Daily and down the road from a Tesco Express, Mr Nader says that its current use as a grocery store is redundant.
Norwich City Council will aim to make a decision on the plans by November 21.