The historic building closed as an arts venue after more than 30 years when its most recent exhibition ended on Sunday.
The Botanics only decided to shut it down last week, sparking a huge public outcry as thousands of supporters signed a petition ahead of a “mass visit” at the weekend.
A senior councillor has now confirmed that talks will take place between city leaders and bosses at the garden.
Lesley Hinds, who represents Inverleith, said: “I’m pleased to see that progress has been made between the council and the Botanics in saving this space.
“As a local councillor, my concern still lies with the release of the report carried out using public funds.
“I will be seeking to make that report public and determine why it wasn’t released in the first place.”