Transport for London (TfL) expects to lose £4bn this year due to the impact of coronavirus.
Ahead of an emergency finance committee meeting, the organisation said it needs £3.2bn to balance a proposed emergency budget for next year.
During the lockdown TfL has lost 90% of its overall income.
Speaking at the committee meeting, Deputy Mayor for Transport Heidi Alexander said the situation was "now critical".
"We have to reach an agreement with the government on this in the next 48 hours," she said.
Ms Alexander warned that TfL may be forced to issue a Section 114 notice - the equivalent of a public body going bust.
"I think the impact of the Section 114 notice is quite honestly unthinkable, with very serious implications for Tube and bus services in London," she added.
A TfL spokesperson said it had done everything possible to help reduce the spread of coronavirus.
"This was the right thing to do and has saved lives," he said.
"It is clear that the long term impact of the coronavirus will mean that we need financial support now and into the future so that we can support the recovery of London and the UK.
"We are in constructive discussions with the government over the necessary financial support."
In the 2019-20 budget TfL set up a reserve of £2.2bn to meet future financial challenges. That year TfL earned £4.9bn from fares, making up 47% of the transport authority's income.
However, the lockdown has led to a 95% cut in people using the Tube compared to this time last year.
The number of bus passengers has also dropped, by 85%, and customers no longer have to tap-in to pay for rides as part of measures to protect drivers.
Most TfL services are still running, but 7,000 staff - about 25% of the workforce - have been furloughed to cut costs.
Unless emergency funding can be found TfL may publish an unbalanced budget, which would ban TfL from spending any new cash.
Conservative candidate for mayor of London, Shaun Bailey, said: "Coronavirus has only accentuated existing problems.
"The 'fares freeze' - that benefitted tourists, not Londoners - cost TfL over £600m in lost revenue. TfL has record debt which stands at £13bn.
"Any bailout must come with conditions - you cannot trust Sadiq Khan with a blank cheque."