Cllr Storey said the meeting had been "very positive indeed."
The move followed yesterday's noon deadline set by transport minister Derek Twigg for Liverpool and Knowsley councils to agree to pick up the entire bill for any future overspend.
On Friday, Liverpool's executive board joined Knowsley in agreeing to support a joint £24m contingency fund for the tram if costs rise above the current budget of around £280m.
But the question now is whether that is enough for the Government, who want guarantees that all cost rises will be met locally, a "blank cheque" that neither district is willing to write.
If the Government is not satisfied, it will not release the £170m it is contributing to the 11-mile route from Kings Dock to Kirkby and the project will collapse.
Merseytravel's plans to build a three-line tram network between now and 2010 have become increasingly troubled over the past year.
But since the Government unexpectedly refused to hand over its £170m contribution to Line One costs, Merseyside politicians have rallied around the tram cause.
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