The Evening News told earlier this week how council officers were set to recommend the closure of Inch House.
The building has suffered a series of maintenance problems and requires extensive work.
A campaign launched to save it has now won the backing of Capital-born Manson.
Asked on social media by the Inch Community Association if she had any comment to make, Manson replied: “This saddens me deeply.”
Plans to close the centre are due to be put before city councillors in May.