Transport secretary Grant Shapps had written a letter to Khan earlier this month listing several conditions in return for any financial rescue package, the newspaper https://on.ft.com/31mAxan reported.
According to the report, Shapps proposed a six-month funding deal to March 2021 dubbed "the H2 deal" ahead of a longer-term settlement.
TfL's income was down by 90% because people avoided public transportation at the height of the novel coronavirus pandemic between March and July. It was bailed out by the central government when its finances came under pressure in the crisis.
The government's proposed deal offered TfL a further 1 billion pounds ($1.29 billion) bailout with demands that the transport operator raise fares and curb the remaining free travel entitlements for children and pensioners, a source familiar with the matter had said on Thursday.
Shapps said the government would take control of TfL and run it from Whitehall if both sides failed to strike an H2 deal or if its terms were not met, the FT said.
Conditions such as extending a £15 congestion charge to the North and South Circular were put forward by the minister.
The demands were rejected by Khan in an interview with LBC News last week.
"Negotiations with the Government continue, but suffice it to say there is simply no way any Mayor could accept conditions of this nature," a representative for the Mayor of London said in an emailed statement on Tuesday in response to the FT report.
TfL had announced last week that government support had been extended for a further two weeks.
(Reporting by Aishwarya Nair in Bengaluru; editing by Grant McCool)
