A TfL spokesperson said: "While there are many details to work through we estimate that there will be a reduction in around 1,000 posts. Our priority is to seek to avoid redundancies by looking at temporary posts and by not filling current vacancies."
The spokesperson said job cuts would be in 'back room' staff, such as human resources, legal, procurement and administration.
"Discussion with unions about London Underground's Operating Cost Review started on 29 January. Frontline operations including train, station and maintenance staff are not part of the review and will be unaffected by any changes," he said.
"The underlying purpose of the review is to ensure that we have an organisation fit for purpose and designed to deliver the massive programme of change and improvement that we have embarked upon."
The RMT Union reacted angrily. General secretary Bob Crow said: "Once again it seems if you are a banker you get protection, but if you are part of a team providing a public service you don't.
"There is no way that London's transport workers should be made to pay for the failure of the bankers and privateers whose greed has created the crisis our economy is now in.
"And there is no way that redundancies on this scale can be implemented with affecting the level of service. If the mayor is looking for efficiencies he should bring the Tube Lines PPP contracts back in house, because they are still draining huge sums of public money from London’s transport budget.
"We make it quite clear that any attempt to impose compulsory redundancies among our members or to undermine their terms and conditions will be met with a ballot for industrial action," Bob Crow said.