Council members voted seven days ago to run the lines to Haymarket, outside the centre.
However, that decision is expected to be thrown out and a recommendation to end the scheme at St Andrew Square to be agreed at a special meeting later.
The trams project, which is over budget and late, has been plagued with controversy and has divided Edinburgh's politicians, businesses and the public.
Earlier this week, the Scottish government said it would withhold £72m of funding if the trams stopped at Haymarket.
The report which comes before councillors said: "The option to complete the project to St Andrew Square is believed to yield the best prospect of a return on investment relative to the original aims of the project and to deliver best value for the city, the council and the Edinburgh Tram Project."
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It goes on to recommend the option to build from Edinburgh Airport to St Andrew Square/York Place be adopted.
The report further recommended agreement to fund the borrowing required "out of current and future resources as set out in the funding proposals and to allow the council flexibility to adopt alternative sources if considered appropriate."
The SNP group abstained last week when councillors voted to end the line at Haymarket, but now the party has said it would back its Lib Dem coalition partners in the new vote.
Labour and Conservative councillors joined forces last week, to reject plans to borrow an extra £230m to run the line into the city centre.
They opted to support a Labour amendment to stop the line at Haymarket.
The Tram Business Forum, made up of city business organisations, said its members wanted to a see a "viable tram route" which would mean the line going to "St Andrew Square at least."
Spokesman for the forum, Andy Neal, stated: "The route must come into the city centre to deliver promised economic benefits to hundreds of city centre businesses which have already suffered substantial disruption to trade, and to create a viable asset for the city."
However an online forum, set up by local resident Eleanor Logan, received over a thousand responses expressing "overwhelming concern" over the council's management of the scheme, the costs and the impact on future services and current reputation.
Ms Logan said: "Whilst there is cautious support for continuation of the project it is not at any cost. We are worried about lack of financial control of the project, the lack of accountability and responsibility for decision making - the future of our schools and services and are not being heard."
See: Funding Withheld From Controversial Trams Project
(JG/BMcC)
