The building, which is a protected structure, was almost gutted by fire damage more than a year ago. The surrounding site, which included the air space above the tracks, and the station building went on the market in 2007, but was not sold.
The RPA have now said that they do not intend to put the site up for sale again given the current market, but will instead lease out the building once renovation has been completed.
Dun Laoghaire Rathdown County Council issued a warning notice to the RPA over the condition of the neo-classical structure in February of last year.
The warning notice referred to the building "continuing to be endangered" and left "open to the elements".
The RPA have confirmed that they have responsibility for initiating the renovation and the letting of the building.
"A contractor will stabilise the building ensuring that there is no further deterioration," Tom Manning from the RPA told the Herald. "We then expect to go to tender for the letting of the building over the next few days."
Mr Manning said that they hoped that these works would be completed and that a new client would be in the building by the end of the year.
The Dublin and South Eastern Railway arrived in Dundrum in 1854 and the original station building was built in 1859 by William Dargan.
Local historian, John Lennon welcomed the overdue renovation project.