Professor Lewis Lesley says using a different type of tram track would allow the controversial scheme to reach its original destination within the £776 million budget.
He says the alternative track type would also mean minimum disruption during construction.
Professor Lesley, who is technical director of light rail company Trampower, met city council transport convener Gordon Mackenzie and senior officials to discuss his proposal.
But council chiefs say they believe the existing consortium led by Bilfinger Berger is “best suited” to deliver the project.
Prof Lesley said the LR55 tram track he proposed for Edinburgh had already been proven a success in Sheffield and was being considered by the US Department of Transportation as a US standard.
He said: “It’s a different technique for laying the track, which means only five per cent of the road has to be dug up instead of the whole road.
“It’s much less expensive because you only have to lay what is in effect a large kerb and the track sits in the kerb.”
Professor Lesley said it would require the minimum diversion of underground utilities, “and it’s much quicker too”.
He accepted work was already under way on relaying the faulty tram track on Princes Street, but suggested the LR55 method could be adopted between Haymarket and Princes Street and between Princes Street and Newhaven.
“It would cost around £10m a mile whereas at the moment it’s about £60m a mile in Edinburgh. You could build a complete metro for that.
“They are going to have about ten trams they don’t need because they are only going to have half the tramway. What do they do with them? They tried to sell them to Croydon, but they didn’t want them.
“It would be a bonus if they could use them as well instead of leaving them to rust in a siding in Spain.”
Prof Lesley, who is professor of transport science at Liverpool John Moores University, was behind private company NETCo, which a decade ago had a £35m plan to run trams around north Edinburgh.
He said he had been in dialogue with the council for the past three months.
He said: “The LR55 track system can be constructed with a minimum of utility works and without having to close important streets.
“All this can be achieved by 2014, and help to restore the reputation of the city.”
However, city council transport convener Gordon Mackenzie said the idea would be going no further.
He said: “We are confident that the consortium we have appointed to build Edinburgh’s tram network is the best suited to fulfil our vision of a clean, modern and efficient system.”
Deputy council leader Steve Cardownie, leader of the SNP group, added:“I think it could be far too late in the day now for a new player to arrive on the scene, but now it’s in the public domain councillors will no doubt be briefed as to the nature of these discussions.”