The 30-year-old has faced criticism for his performances for England over the last couple of years, while he has also lost his place at Man City after being deemed surplus to requirements by head coach Pep Guardiola.
Noble has claimed that Hart "probably deserves a little bit more respect" as the stopper nears a switch to the London Stadium.
"In my opinion, [Hart] has been a little bit hard done by in recent years. He has been fantastic for England and for his club for the last 10 years and he probably deserves a little bit more respect," Noble told reporters.
Hart, who has a contract with Man City until the summer of 2019, spent last season on loan with Serie A side Torino.