The council has announced plans for a special meeting called by the Lord Provost to discuss the funding arrangements for the Edinburgh Tram Project to enable Council officers to implement the arrangements required by the Council decision last week.
The Council is currently legally committed to building the tram line to Newhaven, and negotiations have been ongoing since councillors rejected plans to borrow an extra £230m to take the tram-line into St Andrew Square, as approved by Council at the end of June, 2011.
At a meeting last week, they backed the Labour amendment, deciding to end the line at Haymarket.
The Council has also noted the public statement by the Scottish Government of its intention to review the business case for the shortened route to Haymarket and to consider its position with regard to the outstanding balance of £60m currently payable under the Council's grant agreement with Transport Scotland which is also due for renewal.
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The £60m the Scottish government is considering withholding is the balance of its £500m investment in the scheme, and if ministers act on their threat that could undermine the economic case for the Haymarket option.
It is understood that the Liberal Democrat group on the council will press for a change of heart, urging colleagues on the council to take the trams on to St Andrew Square.
The city's transport convener, Liberal Democrat councillor Gordon Mackenzie, hopes there will be a rethink on the shortened route.
"We clearly thought it (Haymarket) was the wrong option last time", he told BBC Radio Scotland's Good Morning Scotland Programme. "With the costs likely to increase and a considerable question mark over the funding, we're even more convinced that St Andrew Square is the better option.
"Nobody liked the Haymarket option. There was outrage in Edinburgh and elsewhere with it, so, I hope other parties will look at it afresh and come to a different conclusion."
The leader of the city council's Labour group, Andrew Burns, also commented, telling BBC Scotland: "All we are hearing, as opposition councillors, is that, apparently, there has been an increase of £30m, in less than a few days, in the Haymarket option. I can only repeat that I think really serious questions need to be asked of those in charge about why these figures have changed so dramatically in literally a matter of hours."
