Poyet has impressed the academy staff at The Valley, and Powell said that he expects the player's future to remain in London.
"Everyone is looking at Diego and looking at Gus going to Sunderland and thinking he will take his son," Sky Sports News quotes Powell as saying.
"He is someone who we have an eye on to not only have a career but to be involved in this first-team squad. I think people are just trying to drum up stories with Gus going there and the job that he has and whether he will take his son there.
"Gus has been very happy with Diego's development with us and that's the way I think it will [remain]."
Poyet's Sunderland are currently bottom of the Premier League.