Poyet junior is currently on the books at The Valley, with the 18-year-old midfielder highly rated by Powell and his Addicks coaching staff.
They are aware that his obvious potential is attracting interest, and that speculation regarding a switch to Sunderland was always going to be sparked once his father took the managerial reins at the Stadium of Light.
Powell is, however, adamant that Charlton have no intention of parting with Poyet and believe a prolonged stay in south east London would be beneficial to all concerned.
He said in the News Shopper: "Everyone is looking at Diego and looking at Gus going to Sunderland and thinking he will take his son.
"He is someone who we have an eye on to not only have a career but to be involved in this first-team squad.
"But of course Jordan Cousins has made the step up and I have a number of players in that position, but he is one who we feel will do very well at this club.
"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 be."
On the prospect of sending Poyet out on loan, Powell added: "Maybe, maybe not. He hasn't been out yet, it has got to be the right club that plays him in the right position.
"Lads always talk about going out on loan, it is not that easy to firstly place them at the right club but also it is not that easy for them.
"Will Diego go out on loan? Not at this present time, maybe in the New Year if we feel it would aid him. We will have to wait and see."