The 33-year-old defender revealed on Monday that he expects to leave Chelsea in the summer when his contract expires.
Despite some uncertainty over Cole's future, Hartson believes that the left-back will have a string of clubs lining up for his services.
"He was my apprentice at Arsenal, believe it or not. Ashley used to clean my boots," the Welshman told BBC Sport. "He's been a great servant at Chelsea and he's been a great servant for England.
"I thought the way he dealt with being left out of the setup for the World Cup was admirable, very professional. Ashley's got a lot to offer. There will be several clubs thinking that he can still do a job for them and I think he can."
Cole spent the first eight years of his career with Arsenal before joining Chelsea in a controversial move in 2006.