The Evening News revealed last week that bosses at the property arm of Leith Docks have opened talks with a firm that wants to build and operate an arena at Britannia Quay.
It is understood that council bosses still favour the option of persuading a firm to build a massive new indoor arena just south of the airport.
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Senior council sources say an arena on the land, owned by New Ingliston Limited, would be more likely to rival Glasgow's SECC because more people from central Scotland would be on its doorstep.
They say that the road and train network would give it a bigger catchment of potential customers within half-an-hour's commute
, and that even if the tram route is completed to Leith, it will still be too long a journey for many people.
Councillor Tom Buchanan, the city's economic development leader, said: "In west Edinburgh, there will be an additional rail stop, and trams will potentially be out there too.
"It is important that we do get an adequate multi-use venue that can hold a large number of people, that can then be broken down into smaller uses."
He said that the council was "actively progressing" both the Ingliston and Leith Docks proposals in case talks on either "fall by the wayside".
Forth Ports said its talks were with an operator interested in a 5,000-seat arena. The Ingliston facility could be double that size.
Leading figures in Edinburgh's music scene believe that a larger facility in the west of the city would be more likely to be able to compete with the SECC than one at Leith Docks.
John Richardson, who runs Ripping Records, said: "If you do an arena, you would want it to be at least 8,000 (capacity].
"Acts will tend to only have one arena show in Scotland so you would need to be able to attract people from other parts of Scotland.
"While Leith has good facilities, such as restaurants, you have to balance that against the fact that Ingliston is more of a transport hub, in relation to motorway traffic."