The trust called in lawyers to force Capital Gardens from the site after 21 years.
A trust representative said: "We are in discussions with Capital Gardens about the future of the garden centre at Morden Hall Park. As we are speaking with them directly, and with their solicitors, we do not feel it is appropriate to discuss details at this stage."
National Trust said Capital Gardens has made breaches of contract and added that it wants to take over the centre.
Owner Colin Campbell-Preston said: "We are in negotiations with the National Trust. We'll see what happens. We want to stay there." An aquatics concession has already left the site this year.