The structure was bought by businessman Martin Keane
Dublin City Council has issued a letter to businessman Martin Keane, seeking repossession of the Iveagh Markets.
The letter was sent in early January, the council has confirmed.
It has given him until the end of the month to remove his possessions from the building.
The structure on Francis Street in the capital has been listed as 'critical' by An Taisce.
Maintenance for the indoor market was entrusted to Dublin City Council when it ceased operating in the 1990s.
Businessman Martin Keane, owner of a hotel and other premises in Dublin, acquired the site.
In an assessment on its website, An Taisce says: "This building has been vacant for a number of years. This building urgently requires new uses to be identified to prevent further deterioration of its character."
"Most of the external fabric remains, but there are obvious signs of deterioration, particularly water penetration, slipped slates and vegetation growth.
"There is no immediate danger of collapse but the condition is such that unless urgent remedial works are carried out the building will sharply deteriorate."
It was built by the Iveagh Trust, and largely supported by the Guinness Trust, founded in 1890 by Edward Guinness 1st Earl of Iveagh.