The Sunday Times said the Government was preparing to impose the lockdown "within days" after a surge in coronavirus cases in the city.
The paper said Health Secretary Matt Hancock had been examining legal aspects of the shutdown after it was revealed 658 new cases were recorded in the Leicester area in the two weeks to June 16.
The Department of Health and Social Care on Sunday stopped short of saying a local lockdown was likely for Leicester, but acknowledged the city was an area of concern as it urged residents in the city to be vigilant against the virus.
"We are supporting the council and local partners in Leicester to help prevent further transmission of the virus," the spokesman said in a statement.
"We have deployed four mobile testing sites and made thousands of home testing kits available, to ensure anyone in the area who needs a test can get one.
"NHS Test and Trace will contact anyone testing positive to help them identify their recent contacts and advise who may have been near to someone with the virus to stay at home to prevent the spread.
"We urge the people of Leicester to continue to practice social distancing, wash their hands regularly, get tested immediately if they have symptoms and follow the advice they receive if contacted by NHS Test and Trace. This advice is there to protect communities and save lives."
The Sunday Times said Leicester's rise in cases follows an outbreak in food production plants in the area and reports of large crowds gathering outside takeaway restaurants.