Transport for London (TfL) has written to unions stating it could axe around 1,400 jobs.
The body's engineering directorate - which helps maintain the Tube network - is the area set to be chiefly affected.
An RMT spokesman told Transport Network that the loss of TfL's central government grant combined with the fare freeze promised by mayor Sadiq Khan would see spending cut by £5.5bn by 2021.
A letter from TfL to the unions seen by Transport Network confirms there could be around 1,400 'possible dismissals'.
The letter goes on to state: 'The number of actual dismissals is likely to be lower than the number of possible dismissals because it is anticipated that employees will obtain new roles via the selection and assessment process.
'The overall reduction in headcount is dependant on a number of factors to be discussed during consultation but is anticipated to be between 68 and 276.'
A Transport for London (TfL) spokesperson said: 'We are undertaking the largest ever overhaul of our organisation to provide the most efficient and cost effective transport service for Londoners. We have already reduced management layers and bureaucracy and merged functions in other areas to eliminate duplication and reliance on expensive agency staff.
'We do not recognise the RMT’s number. Over the next few months we will be consulting on further plans in a number of other managerial, support and other non-frontline areas across TfL and London Underground. None of this will compromise safety, which will always remain our top priority.'
RMT general secretary Mick Cash said: 'Today all the Tube and tfl unions have been sent written details of the next phase in the wrongly named transformation process across LUL/TFL.
'As part of the Mayor's efforts to slash spending by £ 5.5bn by 2021 we are now being told that the company plan to cut up to 1,400 jobs in engineering in TfL and in some areas of London Underground.
'RMT demands that no cuts take place, so close to the Kings Cross fire anniversary it would be appalling if there was any hacking back on safety.
'The mayor needs to stand up for TfL and demand restoration of the full capital grant and proper central government funding for the tube.'