It is understood about 100 businesses on Princes Street could be the first to receive a 20% discount on business rates or an equivalent package.
For major stores such as Debenhams and Primark, which each pay more than £1.2 million in rates, this would mean a yearly saving of £240,000 apiece.
While the Lothian Region Assessor is considering the claims, it is unclear whether an announcement will be made ahead of the local elections next week.
The troubled trams project is a vital electoral issue in the capital.
Payouts would mean a further financial burden on taxpayers already saddled with a bill of £776m, up from £545m, for the route between Edinburgh Airport and St Andrew Square.
At least 100 more smaller companies in the city's west end are in line to get a rates reduction that will save them between £5000 and £10,000.
Claims are set against the costs of business rates for the coming year, as roadworks continue to disrupt the livelihoods of traders by keeping shoppers away.
It is feared many more millions than could be clawed back have already been lost during the stop-start work, which in some areas has meant digging and refilling in the same site three times.
Most vociferous among the voters are expected to be those along an 11-mile "corridor of contention".
But only those shops which have frontages on to tram works, and can prove loss of earnings, will receive the discount.
Business leaders said they are now more confident than ever that more than 200 firms will receive a rates deal from the independent Assessor.
Graham Birse, of Edinburgh Chamber of Commerce, said: "Up until this point the Assessor has rejected the reduction but as we understand it the Assessor is looking at ways in which it might be possible.
"For an average small business it could be between £5000 and £10,000 a year that could be saved."
He said that Edinburgh city council's backing was significant, adding: "Clearly, there has been a lot of work done on the part of the senior officials at the council and politicians on this, as has been done at the Chamber."
Among those affected is Michael Apter, of card shop Paper Tiger in Stafford Street. Mr Apter, a member of the West End Association said: "The works are of a greater magnitude now than before. The claims in to the Assessor are for a reduction in business rates that reflects the material change of circumstances during the course of the tramworks.
"Parking and access have been greatly restricted and people have been avoiding coming because they don't know if they are going to be able to get through particular streets.
"A change in the rateable value that related to the changes at ground level could mean the difference between survival and not for many sole traders."
Dave Anderson, director of city development for the council, said it is consulting west end businesses and also at Corstorphine, along the tram route, to establish how great the impact has been.
He said that if there was significant evidence gathered, the council would feel "the Assessor will be duty bound to reassess the current rates".
Graeme Strachan, Depute Assessor, said: "There are currently 223 appeals lodged with the Assessor that are seeking reductions in rateable value due to tramwork disruption.
"The rateable values calculated for those properties reflect rental values as at April 1, 2008. If tramworks were being carried out during 2008, and in many cases they were, then the issued values shall already reflect the impact of tramworks.
"We are currently carrying out an investigation to establish whether the current tramworks have further disturbed rental levels that would impact on the rateable values.
"When this investigation is complete we shall consider whether reductions are appropriate and on what basis these should be granted."