With the Grade-B listed art deco building on the market until January 5, the owners said interest had been expressed by a wide variety of would-be buyers.
Peter Fleming, of sales agency Montagu Evans, said: "It really is a bit of a mixed bag. I think it's safe to say the interest is not really for office use because it doesn't really convert well to that. It's more retail, leisure, hotel use among the people who have picked up the phone and spoken to us."
One of the most high-profile bids is from the New Victoria Project, which wants to restore the building and take it back into use as an arts centre.
The Elim Pentecostal Church, which wants to create a theatre, cinema and community facility in the building, is also expected to submit a bid. The church runs a commercial cinema in London's Notting Hill.
Bruce Hare, of the building's owner Duddingston House Properties, estimated that it would cost 5 million to restore to its original condition.
He bought the former cinema seven years ago but his plans to turn it into a hotel were put on ice by a Scottish Government reporter after appeals by Historic Scotland, which said the building should be marketed again in the hope of finding a use which would avoid any demolition.
Mr Hare said: "At the moment we're going through this process, and if somebody can come up with a plan, can demonstrate how they're going to do it and can demonstrate where they get the money from we can move on. There's been a lot of interest. People keep popping up and saying we can do this and we can do that. There's a list of about 20 so we're hoping we'll get a new use for this building."
However, he said the potential buyers would have to prove they could meet the valuation of 2.93m, and if there were no successful bids, he hoped to put his own plans into place.
Duddingston House bought the building hoping to turn it into a venue for entertainment business Luminar, after the two firms renovated and opened The Jam House on Queen Street.
Amid opposition to the prospect of a late-night venue at the location, the firm created its hotel proposal, which involved demolishing the main auditorium, retaining the original foyer and public spaces at the front, and putting a new building around a modern courtyard at the rear.
Mr Hare said: "We have planning permission for the hotel and the objection is from Historic Scotland - there's now an agreement that we market it.
"The issue for me is that this building's going to fall down and there's a risk we'll lose everything rather than looking at something that will retain a lot of it," he said.