One Lower Marsh is being marketed by Savills on behalf of a private investor.
It is being touted as a refurbishment opportunity, with the office space due to become vacant in September 2017.
Current NHS tenants include the Lambeth Clinical Commissioning Group and NHS Property Services.
The building also incorporates the Waterloo Health Centre and several shops including Rymans.
The building currently generates more than £1 million a year in rent for its owners.
"This is a rare opportunity to purchase a freehold, refurbishment opportunity on Lower Marsh, a vibrant, mixed use street in the heart of South Bank," said Simon Ewart Perks, director in the Central London team at Saville.
"The impressive and generous original design provides a unique opportunity for an incoming purchaser to reposition the property to attract premium rents from a range of future occupiers, including those from the creative sector."
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