The glasshouse building, which is part of Parc Tawe, is home to more than 5,000 plants, many of which are extinct from their natural habitat.
Swansea council needs to save £75m over the next three years and closing Plantasia is on the list of new savings proposals.
It was opened in 1990.
Swansea's Plantasia attraction could be closed in a bid to save £400,000 as part of planned cuts by the city's authority.