The Newhaven Heritage Museum - which charts the area's centuries-old traditions of boat-building and fishing - has enjoyed a rent-free home since opening in 1994.
Now owner Forth Ports is demanding 10,000 a year for it to stay following a 2 million redevelopment of the historic fishmarket building.
The council-run museum closed in September 2006 while the refurbishment was carried out. Insiders say the council believes it is being "held to ransom" by Forth Ports and is considering looking for an alternative site.
Today the council said it did not know when the museum might reopen, or even whether it definitely would.
The refurbishment has seen the upmarket Loch Fyne Restaurants open premises on the site where Harry Ramsden's used to be.
The fishmarket building has been completely overhauled and the harbour given a raised timber boardwalk and new lighting.
One source claimed: "Forth Ports doesn't want the museum in the building any more.
"It sees it as a bit of an embarrassment. It doesn't fit into the vision of new bars and restaurants they want to attract to the area."
City culture leader Deidre Brock said: "We are in discussions over the lease of the Newhaven Heritage Museum building.
"Once these discussions are complete, and if a proposed lease arrangement is considered acceptable by the council, we will decide how best to proceed with the internal upgrades and move towards the reopening."
A Forth Ports spokesman said: "We have just spent 2m on a refurbishment of Newhaven Harbour and the fishmarket building that will bring benefits to the whole area.
"We are very surprised that this issue has been raised publicly by the council when we are in the middle of constructive negotiations with them.
"It would be inappropriate for us to comment further while these negotiations are ongoing."
Newhaven's maritime history can be traced back to the early 1500s when part of the coast was bought from Abbot Ballantyne of Holyrood by King James IV.
He created a massive building yard and docks for ships at Our Lady's Port of Grace, as Newhaven was known then, and ordered the creation of the huge warship the Great Michael.
Each port had a distinctive costume and Newhaven women were known as the "yellow butterflies" among Forth fishwives.
A council spokesman said: "A working group is looking at options for the opening of the museum in tandem with ongoing lease discussions.
"Funds have been identified by the council for the refurbishment but this has not yet started. We hope we will be able to open the museum in the near future."