Hartson was born in Swansea and told the Swansea Evening Post: "I am definitely interested in the job and I will be applying for it.
"But I really can't say any more than that because I will be going through the necessary channels."
Another former City striker Dean Holdsworth has been linked with the job but he is expected to stop at Newport County, whom he guided into the Conference last season.
Former Coventry City manager Chris Coleman who said last season that he would not manage Swansea to protect his family living in the South Wales City, is one of the favourites for the job left on Sunday night by Paulo Sousa.
Gary Speed, Brentford Boss Andy Scott and Nigel Adkins of Scunthorpe have also been linked with the job.
Picture copyright of Footy Mad