Today had been described as the project's "drop-dead" day, when it would finally be shelved if a deal to pay for it was not agreed.
But Merseytravel says the ongoing support of the private sector means it has until the end of the month to convince council chiefs to support a payment plan.
Chairman Cllr Mark Dowd said: "We remain confident the scheme will be built and so does the private sector, which has allowed us flexibility in moving forward.
"We are aiming for commercial closure of the scheme by Thursday and financial closure by the end of the month.
"The decision as to whether or not the scheme goes ahead is now purely political."
Merseytravel still has a job on its hands to persuade the five Mersey-side councils to accept a deal to pay for line one.
It has to find between £60m and £65m to add to £170m of government cash so it can build the route from Liverpool city centre to Kirkby.
It wants to use £40m surplus cash from Mersey tunnel charges and has asked Liverpool and Knowsley councils to provide the remainder from money they are due to get from the government later this year.
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