Morden Hall Garden Centre in Morden, Surrey, is holding a £1m sale of stock in readiness for possible closure.
The business, which is part of London chain Capital Gardens, is located within the walled kitchen garden of the National Trust property, Morden Hall. It has operated from there for 23 years, but Capital Gardens has been in a protracted wrangle with the National Trust over its future.
The National Trust does not want to extend Capital Gardens' lease, and intends to take over the running of the garden centre itself.
Colin Campbell-Preston, managing director of Capital Gardens, says he is still unclear about what will happen but that he was taking steps now to reduce stock at the garden centre.
A National Trust spokesman said: "We are in discussions with Capital Gardens about the future of the garden centre at Morden Hall Park and have shared our intention that we would like to take the garden centre into our care.
"As we are speaking with Capital Gardens directly, and with their solicitors, we do not feel it is appropriate to discuss the details of the matter at this stage."
Capital Gardens also runs Alexandra Palace Garden Centre, Neal's Nurseries Garden Centre and Woods of Berkhamsted. It closed Highgate Garden Centre last year.