The gardens have been renovated following a £3.7m grant handed out by the North West Development Agency.
A representative said: "The Japanese and Chinese gardens are restored and new woodland trail, water features and play area are nearly finished. It is all due to open in the spring."
She said the successful agent would tackle upkeep, events and the future evolution of the gardens "to ensure the site never again falls into dereliction".
Alan Carter, a trust manager, added: "This site is special, with a spectacular location, passionate community and iconic past. Many organisations share our views."
The international festival, the first of its kind in Britain, attracted 3.4 million people and became a model for other shows. Years of neglect followed its closure.
Carter added: "By creating a space that is attractive to the local community and visitors we are ensuring the best possible use for the gardens. We expect them to have a positive impact on health, education, social cohesion and the economy."
The managing agent bids are being reviewed and a winner will be announced by the end of the year.