Khan is pushing Osborne to help double the number of homes built in the capital fo more than 50,000 a year.
He warned that the capital's housing crisis had now become a "national emergency that is damaging Britain's economy and productivity".
"I grew up on a council estate built by a government that understood that building affordable homes is good for Britain's economy. But London's housing crisis is now a national emergency that is damaging Britain's economy and productivity," Khan said.
"The government must use the Budget this week to take emergency action to build the genuinely affordable homes that Londoners need," he added. "This package of measures would give London government the tools it needs to get on with the job of fixing London's housing crisis."
In particular, Khan wants the government to devolve new powers to London in the Budget to ensure a change in the number of homes built in London.
The Tooting MP wants City Hall to gain control of all surplus public land in the capital, as well as asking that the mayor keeps a portion of the stamp duty raised in London to spend on housing, as recommended by Lord Kerslake’s London Housing Commission last week.
As part of the drive, Khan also wants to take action to prevent land banking, support a new construction skills academy and boost to government investment in London's housing.
Khan also wants greater transparency over property and land ownership to end the use of offshore holding companies to disguise the identity of ownership and wants councils to be permitted to invest "prudentially in new social homes".
The push by the Labour MP comes after a recent poll that put Khan ahead of his Conservative rival Zac Goldsmith by five points.
The results indicated, however, that the race is still relatively open, with a quarter of Londoners saying they have yet to make up their minds and the margin between the leading candidates much closer in outer London.