Campaigners claim the proposed sale of The Lawn is being pushed through without proper consultation.
The City of Lincoln Council announced plans to sell the site of the former asylum in Union Road, Lincoln, in October.
Leader Ric Metcalfe blamed rising maintenance and running costs in a tough economic climate.
Also for sale is the Sir Joseph Banks Conservatory – named after the eighteenth-century Lincolnshire botanist – plus shops, offices, café units and some parking spaces.
The council now says it will begin advertising the sale in early January, with bids invited until the end of February.
But more than 2,000 people have signed a petition to keep everything apart from the main building in public hands.
West End resident Emile van der Zee, who is fronting the Hands Off Our Lawn campaign, said: "What I'm against is that it's being pushed without any proper consultation.
"It was announced that there would be a consultation but there has not been, there were just two small adverts in the Lincolnshire Echo.
"They thought they could push it through without giving people time to comment on it and I think that's not really the way to go forward.
"There are many people who are interested in looking at the area again and what the area can mean for people in Lincoln.
"What has not been looked at is how it could be developed for tourism.
"Is there anything we can do to see if The Lawn can generate an income?
"If there are people who are prepared to do a little bit, maybe we can come up with a decent project."
All short-listed bidders will have to put their case to a panel made up of the leader of the council and senior legal, property services, economic development and planning officers.
The authority has stressed that it is not simply looking for the highest bid, rather, a plan that will address future uses, along with conservation and planning issues.
Marie Diamond, 44, runs the Come to Life gift shop in the grounds and manages the conservatory.
She has a petition and comments book at the conservatory which attracted more signatures during the Lincoln Christmas Market.
She said: "The panel that will decide the future of The Lawn is made up of the leader of the council and senior officers.
"What about the public?
"There's no power to the people – we have no influence in the process.
"With permission from the council, I sold teas and coffee at the conservatory during the Christmas Market.
"I'm now in a position where I can make a donation to the Lincoln swan charity.
"That proves it can be run commercially."
Running and maintaining the site costs council taxpayers £47,000 a year.
And there is an additional £100,000 worth of repairs and improvements needed.
Leader of the city council, Ric Metcalfe, said the authority has written to tenants to keep them fully informed about the plans for The Lawn.
"We will be carrying out a very detailed evaluation process, ensuring that the sale is in the best interests of the people of Lincoln," he said.
"We will not base our decision to sell on price alone and any sale will be subject to the leases of existing tenants who currently occupy premises at the complex."