The Sunday Times also quoted sources close to London's transport body as saying the move was encouraging and suggested the possibility of talks.
"While we haven't been asked to make any changes, we'd like to know what we can do," Tom Elvidge, Uber's general manager in London, told the newspaper. "But that requires a dialogue we sadly haven't been able to have recently."
A spokesman for Transport for London (TfL) declined to comment.
The Sunday Times said Uber's concessions were likely to involve passenger safety and benefits for its drivers, possible limits on working hours to improve road safety and holiday pay.
TfL stunned the powerful U.S. start-up on Friday when it deemed Uber unfit to run a taxi service for safety reasons and stripped it of its licence from Sept. 30, although the company can continue to operate while it appeals.
The regulator cited failures to report serious criminal offences, conduct sufficient background checks on drivers and other safety issues.
By 2200 GMT on Saturday, more than 600,000 people had signed although it was not clear how many of them were in London.
A spokesman for Uber said around 20,000 Uber drivers had emailed the city's mayor directly to object to the decision.
(Writing by William Schomberg; Editing by Marguerita Choy and Paul Simao)
(Except for the headline, this story has not been edited by NDTV staff and is published from a syndicated feed.)