New data released today showed that 6.6 people in every 100,000 in Leeds are known to have contracted the virus over the last seven days.
It means the city has a low infection rate compared with the national and regional average.
A health scrutiny board heard on Tuesday that there is also no evidence of localised outbreaks in any part of the city.
But officials are wary of the much higher infection rate in neighbouring Kirklees and in Bradford, where the data suggest 38 people in every 100,000 have tested positive for COVID in the last week.
Speaking to councillors at the board meeting, Leeds' director for public health, Victoria Eaton said: "At the moment we're getting around 40 new positive cases a week, though sometimes it's up to 50.
"It's been falling recently.
"We've no evidence of community clusters or spreads in any particular communities.
"One of the issues in areas where the infection rate is very high is community spreading, which is hard to manage.
"I can report we've no evidence of community clusters in Leeds at the moment."
Ms Eaton said Leeds was involved in talks about tackling the high infection rate in surrounding areas, adding: "It matters to us what happens in the rest of West Yorkshire."
It was also revealed that officials are "keeping an eye" on the risk of people living in Leeds bringing the virus back from their workplaces in neighbouring towns and cities.
Among the 170 staff who tested positive for COVID at a meat factory in Cleckheaton last month, 28 were Leeds residents, councillors were told.
Ms Eaton also said that while the rate of infection is expected to remain "stable" throughout the summer, an increase of some kind is expected to take place this autumn and winter.
On Monday, the government made wearing masks in shops a legal requirement from July 24, but the public is also being reminded of the importance of handwashing.
Ms Eaton added: "There's a huge range of different scenarios we need to be working to.
"A lot depends on how engaged the public is in doing the things that will make a difference.
"The most evidence we have for stopping spreading is around regular handwashing, so I'm hoping the basics like that don't get overtaken by the debate around masks.
"I've just come off a call with the chief medical officer, Chris Whitty, and they don't know what scenario they're looking at.
"They're planning for an increase but they don't know what that will be at this moment in time."
Local Democracy Reporting Service