The letting of the nursery will bring to an end 25 years of bedding growing in the parks - 60 per cent of the bedding is currently grown there under contract by RA Meredith - but could see the sire redeveloped as a garden centre or other facility.
The Grade II-listed Magazine in Kensington Gardens and the nursery in Hyde Park are being offered through estate agent Knight Frank.
A Royal Parks representative said: "Potentially all our bedding plants would be bought in if the nursery was to be developed."
The sites could be redeveloped as art galleries, garden centres, museums or cookery schools. Properties are not for sale, but the agent is asking for "submissions of interest", which could lead to a standard tender process and a licence to use them for 10 to 20 years.
The two sites have been identified for potential redevelopment as part of the Royal Parks' Better Buildings Programme, which aims to raise funds to improve the facilities and services offered. The programme has already brought about the refurbishment of seven parks lodges for short-term residential lettings and two more will follow this year.
Office staff who work in the Magazine would move to other parks buildings if redevelopment goes ahead. Proposals will be subject to planning and listed building consent, and comply with the objectives of the Royal Parks.
Knight Frank partner James Leaver said: "The potential is very exciting and the Royal Parks is committed to looking seriously at all proposals - no matter how quirky."
Royal Parks chief executive Mark Camley said: "Making better use of our buildings is an excellent way to ensure value for money to the taxpayer by generating income to invest back into the parks for everyone to enjoy. We are seeking proposals that demonstrate a high standard of architectural, landscape and environmental design, and complement the park setting and values."
Interested parties should contact Knight Frank by 28 November.