Mayoral sources said the city was catching up with disease hotspots in the North West and North East of England, which have been placed under new controls.
While data from only a few days ago suggested London was two weeks behind those areas, the latest modelling seen by Mr Khan was said to show the gap had closed to two or three days.
The mayor is now urging ministers to extend the latest regional restrictions – including ordering bars and restaurants to close at 10pm – to cover the capital as well.
Government and City Hall officials are thought to be meeting this afternoon to discuss possible new restrictions on the capital.
Matt Hancock said he had spoken with London Mayor Sadiq Khan over the weekend about what action is needed in the capital.
Asked if London office employees could be advised to work from home from some point next week, Mr Hancock told Times Radio: “Well, I wouldn’t rule it out.”
Such a move would be in contrast to the Government’s recent messaging, which has been urging people to get back to their offices following the easing of lockdown restrictions.
Mr Hancock was asked on Sky News about comments from Mr Khan that restrictions in the capital were increasingly likely.
He said: “I’ve had discussions this week with the Mayor of London, and the teams are meeting today to discuss further what might be needed.”
A mayoral source told HuffPost: “It’s clear that cases in London are only moving in one direction, we are now just days behind hotspots in the North West and North East. We can’t afford more delay.
“Introducing new measures now will help slow the spread of the virus and potentially prevent the need for a fuller lockdown like we saw in March, which could seriously damage the economy once again.”
He is also said to be looking at the possibility of asking those who are able to work from home to do so.
Such a move would be in sharp contrast to the Government, which has until recently been urging people to get back to their offices following the easing of lockdown restrictions.
It comes as people in England who refuse an order to self-isolate will face fines of up to £10,000, the Government has warned amid deepening concern at the sharp upsurge in coronavirus infections.
In a significant toughening up of the regulations, ministers will impose a new legal duty on people to self-isolate if they test positive for the disease or are told to do so by NHS Test and Trace after coming into contact with someone with the virus.