His comments came after it was revealed that it would cost about ?750m to cancel the project - more than ?200m over the original budget of ?545m.
Mr Salmond said some parties would have more to fear from an inquiry than others.
SNP MSPs have always opposed the controversial project.
An Edinburgh City Council report on the trams is due to be revealed on Thursday afternoon, but some of the figures were leaked a day early.
It is understood that the report estimates it would cost ?700m to build the line from Edinburgh Airport to Haymarket, west of the city centre, and ?770m to complete the route to St Andrew Square in the city centre.
Councillors will decide the fate of the project at a meeting next week.
The original budget of ?545m had been the figure for running the line through the city centre and on to Newhaven in the north of the city.
A contractual dispute between the tram company Tie and contractors Bilfinger Berger pushed the project over budget and behind schedule.
Mediation talks are understood to still be under way after the initial meetings between Tie and Bilfinger Berger were held in Glasgow in March.
In May, a report published by Edinburgh City Council said work so far had cost ?440m - about 80% of the original budget - with huge sections of the line still to be completed.
Edinburgh councillors ordered a report to be written by officials into the estimated costs of scrapping the tram project.
A full council meeting will be held on Thursday 30 June to decide the future of the scheme.
When the news was leaked on Wednesday, Andrew Burns, Edinburgh City Council's Labour leader, also called for a public inquiry into the tram project.
An Edinburgh City Council spokeswoman said: "The costs associated with the various options for phase one of the tram project are still subject to commercial negotiations and legal scrutiny.
"In accordance with the outcomes of the mediation process in March, we cannot publicly divulge these figures until both parties have agreed to do so.
"Members are, therefore, being given this confidential information to help them make informed decisions at next week's council meeting and we will ask them not to disclose this to ensure we comply with the mediation process."
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