Martinez Wines has applied for permission to move into an empty unit previously occupied by Bagel Nash, in the city’s Thornton’s Arcade.
The business, which according to its website was started in the early 1980s, sells wine and tapas at its own bars in Ilkley and Bingley.
Bosses have now requested an alcohol licence from Leeds City Council to serve until 11pm from Sunday to Thursday and until midnight on Friday and Saturday.
Customers would also be able to buy bottles to take home, under the proposed terms.
Two nearby business owners have objected to the licence, however, with one citing concerns around serious anti-social behaviour in the surrounding area.
The matter is likely be decided at a public hearing next Tuesday.
In an email to the council, one of the objectors said: “Throughout the day, mainly after business hours, this is known as a hotspot for drug related problems, drunken disorderly antics as well as anti-social behaviour.
“People smoke here, urinate, fight, use drugs as well as loiter, which is extremely concerning as a business owner.”
They added: “I run a business which involves the loading and unloading of stock regularly after 7.30pm.
“The problems stated above are already a health concern/risk, and it is important you understand bringing this application to my establishment will only continue to be detrimental to my business.”
In their application form to the council, Martinez’s representatives said: “The applicant is pasionate about promoting the enjoyment of high-quality wine.
“Their ethos, offer and pricing all supports the responsible consumption of quality over quantity, without adverse impacts upon licensing objectives.
It added that this was, “Demonstrated by the smooth operation of their Ilkley and Bingley establishments, which are valued by the communities they serve.
“They do not and will not serve shots, cocktails or alcopops.”
Neighbours of the firm’s bars in Ilkley and Bingley have also offered support to the application, while Bradford Council’s licensing enforcement team said they’d had no issues with either premises.
In a written submission, neighbour Lorraine Hurlstone said of the concerns around anti-social behaviour, “I would like to assure you and the objectors that, in my experience, Martinez Wines do not contribute to such issues in Ilkley.
“I’m confident they will maintain their high standards and good reputation in Leeds and that they will enhance the Thornton’s Arcade.”
The former Bagel Nash premises, which opens out onto Swan Street, has been empty for around a year, according to the application form.
A panel of three city councillors will have the final say on whether or not to approve the licence.