An updated report on the project to be put to the full council meeting is understood to recommend the £162 million scheme should not get the final go-ahead at this stage.
But the report is also expected to propose the council goes ahead with “enabling work” on Leith Walk and the purchase of land at Granton needed for a potential future extension of the line there.
The council’s powers to acquire the land under compulsory purchase will expire in May next year. The proposed extension of the tram route from its current terminus at York Place to the previously planned “end of the line” at Newhaven was approved in principle by the full council on November 19.
But a division within the ruling Labour-SNP coalition meant a decision on ordering work to start was postponed until the next full council on Thursday next week.
A working group made up of four senior councillors from each side was appointed to follow up the concerns expressed about the project, including the robustness of the financial case for the extension.
Now it looks as if those with concerns have won the day and persuaded colleagues this is not the right time to embark on the scheme.
A source said the whole question of the extension was effectively being postponed and it could now become an issue for the next council elections in 2017.
But a compromise appears to have been struck which allows preparatory work to continue over the next 18 months.
The source said: “The report recommends not proceeding with the tram extension at this time, but other aspects such as the land at Granton may need to be pursued.
“It will be for the new administration to decide whether to take the tram to Newhaven. It’s something you could expect to see in the parties’ manifestos.”
Memories of Edinburgh’s original tram project – five years late and twice the price for half the line – are strong.
However, Labour leaders have argued the tram extension would boost the Capital’s economy, provide fast transport between key parts of the city and help the development of the waterfront area.
The SNP has claimed the financial case was not robust enough and has said the extension should not go ahead when the council plans to make massive spending cuts, including 2000 redundancies.
There were also concerns about the plan to finance the initial stages of the project from a proposed £20m “extraordinary dividend” from Lothian Buses.
The council instructed officials to find out what impact such a large payment would have on the company in terms of fares and future investment.
An extension to Newhaven would take six years to complete, according to the plans put to councillors, with construction not even getting under way for two-and-a-half years.
The Conservatives opposed the extension in principle, arguing it was too expensive and would take too long.
They also questioned if the council was equipped to carry out such large projects. If Labour was determined to press ahead with the project, it could expect the support of the Greens and the Liberal Democrats, which would give them enough votes to push it through.
But Labour sources said they did not want to threaten splitting the coalition.