The pub – which appeared in the 2013 film Sunshine On Leith – is renowned the world over as it started life as a place for sailors to drink when they docked in Leith.
It also built up a reputation thanks to its legendary former landlady Mary Moriarty, who ran the pub for 25 years.
Locals – who fear it may end up closing – have already vowed to save the pub, with talk of fundraising events to help reverse its current fortunes.
The message read: “I’m sorry to say it has actually come to this.
“The pub has been facing a lot of adversity this year, with rising costs, and a very big repair bill recently, compounding other problems.
“In order to negate some costs with Punch they have offered a concession on the rent if we make the pub available on the open market.
“I’m sure there will be a lot of questions, and hopefully we’ll get round to answering as many of them as possible in the coming week.
“I want to clarify that we are still open, and for now it’s business as usual. If there are any changes we’ll let you know.
“I’m sorry that the pub so many of you love is facing an uncertain future.
“With such devoted staff and customers it deserves better.”
Ms Moriarty, who is still a regular in the pub, said the Port O’Leith had a place in locals’ hearts and she would be sad to see any drastic changes.
“The customers make it a brilliant pub, as well as the ambience,” she said.
“But Leith is a different place now and if they’re not making money, what can you do? I expect Punch will keep it open until they acquire someone else to take it over.
“It would be a shame if it closed”.
A spokeswoman for Punch Taverns said: “Punch Taverns are currently recruiting for a new tenant to take the long- term opportunity at the Port O’Leith Bar in Leith.
“Once successful we hope to complete a sympathetic investment retaining the unique character and atmosphere which lies at the heart of this landmark pub. Until this time the pub will continue to trade.”