The local authority is inviting expressions of interest from groups willing to take on the 40-year-old free visitor attraction. Gardens manager Chris Kidd said: "I'd like to see the garden continue to be run as a botanic garden and that's what the expressions have shown, so it's positive."
He added that the garden attracted around 270,000 visitors a year and Ventnor was developing its website and an e-commerce site. It is also extending its olive grove and, for the first time, offering a scholarship.
Kidd was head gardener for 11 years and has five gardeners, although five staff were made redundant in the summer. The site, which previously hosted a hospital, features subtropical plants.
A council representative said: "Because of the financial pressures we face, the council is no longer able to run Ventnor Botanic Garden to its full potential."
The closing date for applications is 11 November at firstname.lastname@example.org.