Speaking to the BBC’s Local Democracy Service, Khan said he is asking for “roughly” £1bn for a City Hall developer fund that will help construct 16,500 homes.
It comes weeks after Chancellor Rachel Reeves allocated a further £100m to the £4bn affordable housing fund in her Budget.
The mayor was given a goal by the last Conservative government to start work on 35,000 affordable homes by March 2026.
The target was slashed last year to a range of between 23,900 and 27,200 homes as costs rose.
However City Hall has only started work on 2,124 homes, meaning it is currently less than a 10th of the way towards hitting the lower end of the already-reduced target.
The programme is also a third of the way through the time available since receiving £4.1bn funding in July 2023.
City Hall Conservatives say if the mayor continues at the current rate of progress it will take him more than 30 years beyond the deadline to hit the target
"We think £1bn, roughly speaking, can lead to the construction of 16,500 homes – around half of them by 2027," he said, adding he also wanted the government to "give councils the ability to borrow to build".
He also told the service: “The amount of grant we would be giving to a council or a registered social landlord, to build an affordable home, is now much higher than it used to be.
“It’s going to be challenging, in relation to the target we’ve got with the government. We’re going to make sure we do everything we can to get these affordable homes built.”
The Ministry for Housing, Communities and Local Government said it "will work in partnership with the mayor of London to tackle the housing crisis and deliver the homes that London needs".
A spokesman at the Ministry for Housing, Communities and Local Government said: “We know that we must radically boost housebuilding in the capital.
“That is why we will work in partnership with the mayor of London to tackle the housing crisis and deliver the homes that London needs.”