The mayor, who claims that the PPP breaches European state aid rules, has 74 days to appeal against the European Commission's decision to back the deal, starting from when it is published this month.
The London Underground source said an indemnity, which would underwrite the consortium's bid costs if Ken Livingstone won the appeal and further delayed the projects, was unviable.
The source said: "I think they have no chance of getting it – it's the wrong time to be trying to do this.
It will take months to work out the exact structure of an indemnity deal – it would be a huge agreement in itself."
The source said the discussions over indemnities were threatening the whole part-privatisation. He said: "The consortiums are risking the government walking away from them by trying to get these assurances. We expected this to be sorted out this week; the mood at London Underground is quite despondent right now."
The issue of Livingstone's possible appeal has dogged both teams reaching financial close on the schemes.
Contracts were due to be signed last week but will now be delayed for at least a month. Tube Lines is expecting to sign early in December, but Metronet is not due to reach financial close until early February, as it has yet to secure funding to the tune of £2.6bn.
The consortiums are risking the government walking away from them
London Underground source
London Underground wrote to Transport for London chief Bob Kiley last week to confirm that the completion of the two deals would be split, as predicted last week in Building.
A source at Metronet, which includes Atkins and Balfour Beatty, said discussions over possible indemnities were taking place. The source said: "The government is trying to come up with a mechanism that will be satisfactory to back-stop the state aid judicial review. However they dress it up, it will need to be an indemnity."
The indemnity call was backed by Tube Lines, which includes Jarvis, Amey and Bechtel. A source at Tube Lines said: "We are not shouting it with a megaphone but [the indemnity] would make the deal more straightforward."
A Department for Transport spokesperson confirmed talks were under way. He told Building: "The government is in discussion with the businesses over how to find a way through this. We cannot be specific as to what the discussions are, as that would compromise the negotiations."
The spokesperson insisted that the government still intended to press ahead with the deal, despite Livingstone's warning this week that the PPP was "going up the Swanee".
The spokesperson added: "Both ourselves and London Undergound are working hard to deliver the deals."
Ground to a halt: More delays for the Tube PPP18 October
Building reveals Metronet is facing delays to signing the deal because it can’t finalise funding. Banks are nervous that London mayor Ken Livingstone will appeal the European Commission’s decision to clear the deal. 22 October
Tube Lines denies Amey’s financial woes will harm its ability to sign the PPP refurbishment contract. 4 November
Metronet admits it is struggling to raise the £2.6bn it needs. 8 November
Tube Lines lobbies the Treasury to allow it to sign off its deal without having to wait for Metronet. Livingstone claims the cash-strapped Tube companies will disappear “up the Swanee” as the process drags on.