Noble says the competition for a starting spot among the keepers at West Ham will increase if Hart arrives as he contends with Adrian and Darren Randolph, and called for the 30-year-old to be given more respect.
"I've known Joe for a long time, we played for England U21s together years ago," Noble told Sky Sports.
"He is obviously a fantastic goalie but at the minute he is not our player. We have got two really good goalies here so it would be more competition for them.
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"In my opinion, he (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."
British media reports claim Hart will undergo a medical at West Ham on Monday and is close to completing a deal ahead of the team's pre-season fixtures, which begin on Thursday against Championship side Fulham.
(Reporting by Aditi Prakash in Bengaluru)
