The City of Lincoln Council is looking to lease the use of The Lawn venue for three years after it failed to sell.
The council is inviting expressions of interest for the lease and operations of the Lincoln Suite and premises inside the former asylum.
Existing leases for business units on the site remain unaffected.
In a statement, Andrew Taylor, chief executive of the City of Lincoln Council, said:
"The Lawn is an important city asset but one that, in these times of central government cuts, is proving increasingly difficult for the city council to maintain.
"It is important that we keep the character of the building, and the surrounding grounds must remain open for the people of the city to enjoy.
"Last year we placed the property on the open market but it is a reflection of the economy that it did not attract sufficient bids. More importantly, we were unable to achieve the necessary assurances we were looking for with regards to protecting the public open space.
"The property ultimately remains for sale, but in this difficult climate we are realistic about the prospects for this.
"We have, therefore, turned our attention to ensuring that The Lawn continues to be an important part of the offer in Uphill Lincoln, particularly as we approach the Magna Carta celebrations in 2015.
"We are also very mindful of the need to maintain a viable trading environment for the other businesses located at The Lawn.
"We are, therefore, inviting tenders to be submitted for a lease to operate the premises for a three-year period."