At the moment the supermarket has a 24-hour licence to sell drink and, although it is a 24-hour store, it currently closes at 10pm on a Saturday night and is also only open from 10am to 4pm on Sundays.
Now, Tesco has submitted a new application to Sheffield Council for a 24-hour drinks licence and has also told the council that it intends to extend its opening hours on Saturdays by two hours, meaning it would be selling alcohol until midnight.
These plans have met with anger from local residents and ward councillors, who say there are already "very substantial noise issues relating to the store."
Coun Sylvia Dunkley, who has objected to Tesco's licence application, said: "I would ask that grant of the premises licence should be for the existing opening hours, rather than any extended period.
"This would continue to provide Marriott Road residents with hopefully one definitely undisturbed night in the week."
One resident of Marriott Road, who has also submitted an objection to Sheffield Council's licensing board, said: "We are vehemently opposed to the application. The supermarket is adjacent to the Sheaf Valley walk.
"The riverbank side of the walk is frequently littered with dozens of empty lager cans deposited by late-night drinkers.
"In the summer months particularly, a 'camp' sometimes develops on the meander near to the store entrance. Opposite the meander is a rope swing over a fairly deep section of the river.
"Thankfully, no serious incidents as yet, but it is not inconceivable that some alcohol-fuelled individual will, in the future, end up in the water and get into difficulty.
"On occasions late-night revellers make their way noisily along the Sheaf Valley walk. Marriott Road overlooks the walk.
"We get woken by them but hope that they pass quickly on to their destinations.
"Mostly they do but, given the opportunity for alcohol refuelling at Tesco if the application is granted, then we will doubtless be subjected to much more disturbance.
"To extend the time that alcohol could be purchased at night would not be a particularly responsible course of action."
Another Marriott Road resident told the licensing board: "We strongly suspect that this application, if granted, would encourage further anti-social behaviour in the Sheaf Valley walk, which is very close to Marriott Road, and which would therefore have a big impact on local residents.
"In addition, we are concerned about an increase in traffic and of people drinking in the vicinity of the store.
"In the past couple of years, the junction (of Abbeydale Drive and Abbeydale Road) has been the site of a number of road traffic accidents, several of which to my knowledge have been incidents involving pedestrians.
"The likelihood of this kind of incident is surely increased by out-of-hours alcohol sales at the Tesco store."
Members of Sheffield Council's licensing board will make a decision on Tesco's application at a meeting which begins at 10am on Thursday, November 11.
In the application to the council, a spokesman for Tesco says that the supermarket is a "national retailer that sells alcohol as part of a broad offering of goods and services."
The application adds: "All staff will be trained and regularly refreshed in the corporate Think 25 policy. Staff will be trained to look at the customer and 'Think 25' when selling alcohol."
A spokesman for Tesco said: "We are applying for an update of our existing licence.
"We are a responsible retailer of alcohol and look forward to continuing our good relationship with the local community."