An addition to the existing 14km (8.7-mile) tram route had long been touted as one of the infrastructure projects which could be financed through the £1 billion-plus package of investment from the UK and Scottish governments.
The City Deal, which also covers the other three Lothian councils and Fife and Borders, has yet to be unveiled.
But the Evening News understands Scottish ministers have vetoed using any of the cash for a tram extension.
Councillors are due to decide soon on whether to go ahead with an extension down Leith Walk and on to Newhaven, last estimated at £162 million.
Senior council sources indicated that in the absence of City Deal funding, the extension could be paid for by borrowing money and repaying it from future fare revenues.
The council already has an agreement with Lothian Buses that the council-owned company will provide a £20m extraordinary dividend to help fund the project’s initial stages.
The tracks for the extension to Newhaven were bought as part of the original tram contract, before the route was curtailed as costs soared. The tram vehicles were also bought.
A final decision on whether to go ahead was postponed until after the council elections.
Labour fought the May 4 local elections saying it wanted to go ahead and complete the line. The SNP backed the idea in principle, but said it would only press ahead if there was a robust business case and disruption was kept to a minimum. The Tories argued the project, as proposed, would cost too much and take too long to complete.
Tory group leader Iain Whyte said the exclusion of the tram extension from the City Deal came as no surprise.
“The tram extension has always been in the realms of the politically controversial and I’m sure all parties to the deal will want to see it as overwhelmingly positive.
“I believe there should be a fresh look at whether the tram extension is affordable. The capital costs in the business case are exceedingly high – those really do need to be reviewed.
“The Edinburgh public would not forgive us if they saw us throw money at something on the basis it would make the route profitable in the long-term. It has to make sense in terms of the capital costs.
“If it is not part of the City Deal it allows the newly elected council to review it properly and come to a reasonable conclusion on whether some can be done in a reasonable timescale and at reasonable cost.”
SNP group leader Adam McVey said: “The SNP believes the tram extension will be a positive investment for the city, but we think it can and should be self-financing and we are looking to make the investment along these terms.”
A council spokesman said: “Discussions are ongoing with the UK and Scottish governments with a view to securing a City Region Deal.”