Anne Mulhern, who has run the Sauchiehall Street business for 30 years, is now desperately trying to find a way to save the operation and the jobs of her 25 staff.
She sub-lets the first-floor tea room, which was designed by Charles Rennie Mackintosh, from Henderson the jeweller which trades from the ground-floor unit.
But the jeweller has announced it is to close down, putting the future of the Willow at risk.
Ms Mulhern says to save her business, she must either renegotiate the lease of her premises or persuade the owner to sell up.
Failure to reach agreement with the bank which owns the block where the tea room is based could result in it closing by the end of May.
Ms Mulhern said: "My lease is with Henderson's, but this week they put up a notice saying they are holding a closing-down sale.
"They are talking about leaving at the end of May so it is a bit scary."
An added problem for Ms Mulhern is that a survey of the restaurant found it is no longer wind and water tight and needs around £450,000 of urgent repairs.
The Willow, which is housed in a A-listed building, was designed by Mackintosh in 1903 and served as a tea room as well as having a number of other uses until it was restored and reopened in 1983.
Ms Mulhern has run it ever since and says she will fight to save it from closure.
She said: "I cannot walk away from the tea room. I've been here for 30 years – it is my baby."
Today it was revealed senior city council officers are to meet Ms Mulhern at the Sauchiehall Street premises next week.
Liz Cameron, the council's executive member for jobs and the economy, said: "I am keenly aware of the importance of our built heritage.
"As we do not own the property, there is a limit on what we can do, especially in the challenging financial climate.
"However, we will offer what support or advice we can, such as referring the owner to any historic building property grants, or other appropriate assistance."