City of Edinburgh Council is making "every effort" to secure a future for Gorgie City Farm, according to its leader.
The well-loved attraction collapsed last week with the loss of 18 jobs.
Liquidators were called in on Friday but after meeting the insolvency practitioner, council leader Adam McVey said the response from interested charities was "encouraging".
Liquidators have not specified the cause of the farm's financial collapse.
Gorgie City Farm first made council officers aware of their situation on 31 October and an insolvency practitioner was appointed the following day.
Mr McVey met liquidators on Tuesday, then spoke to local elected members, MSPs, community representatives and former staff on Wednesday.
He said: "We are working with the insolvency practitioner to make every effort to secure a future for the farm in Gorgie which has provided a valuable experience for adults and children across the city for many years.
"The insolvency practitioner must now be given time to work with interested parties and it is unlikely that we will find out more until at least the end of next week."
He said it was "very encouraging" that several credible charities had expressed interest in taking over the farm, and praised the positive response to a crowdfunding initiative.
Mr McVey promised that animals on the site, including livestock, would not be slaughtered.
Gorgie City Farm gave volunteering opportunities and support to disadvantaged young people and adults.
It welcomed about 200,000 visitors a year since it was saved from closure in 2016 after a crowdfunding appeal raised in excess of £100,000.
MHA Henderson Loggie has been appointed to wind up the farm, which has about 50 livestock and 50 pets.
They include sheep, pigs, ducks, geese and chickens and a number of smaller animals including snakes and lizards.
The farm received funding from City of Edinburgh Council, various trusts and individual donors. Its cafe and animal boarding service also generated income.
It chairman George Elles blamed falling revenues due to a decline in external funding and rising costs.
The farm was in the news four months ago when it was visited by the Queen.