Reports in the last 24 hours suggest Hirst has emerged as a transfer target for the Toffees, who are looking to bolster their Under-23 squad.
Hirst, who turns 18 next month, made his senior debut for the Owls as a substitute in their League Cup defeat to Cambridge United.
Carvalhal says the youngster, who is the son of Owls legend David, is integral to his long-term plans.
“George is our player for the future and we have a plan for him,” he said.
“The worst we can do is try to put him in the first team too fast. He is not ready.
“He is a big talent but he must play in the correct moments. To play at Under-23 is the standard he needs, against seniors.”
Several top-flight clubs are believed to be tracking England Under-18 international Hirst, who penned his maiden pro contract last March, keeping him at Hillsborough until the summer of 2018. It is understood the Owls are keen on tying Hirst down to a longer deal.
“George is under contract and more importantly wants to be here,” he said. “The player, his father is a legend at the club, and the boy likes to be here and loves the club.
“The wishes of the player will drive everything in the future, if he wants a career here.”
Wednesday were handed a big boost earlier this week when key duo Sam Hutchinson and Fernando Forestieri extended their Owls stays. Defensive midfielder Hutchinson and striker Forestieri have agreed deals until 2020.
Carvalhal said: “It is very good news. We are trying to build a solid team with players that will be here for years.
“We want to create a good vibe. These two players belong to this family. They have value, ambition and can do well in the future.
“These players are not the type who are happy because they have signed a contract and stabilised. Their personalties mean they want more, push the club, win games.
“That’s very important to the future because I think we have a player base of good value for the next three or four years.”
It has been a rollercoaster campaign for Forestieri but Carvalhal is convinced it is only a matter of time before he rediscovers his best form.
“It’s not been a normal season (for Forestieri),” he said. “In the beginning he had problems, then in December he didn’t play in four games.
“But he gave strong signals that before his red card he was playing at the right level. He is doing better game by game, and I believe on Saturday against Huddersfield he can get near to his best level.
“Fernando is a fantastic player.”
Meanwhile, out-of-favour striker Sergiu Bus has joined Romanian side FC Astra Giurgiu on a permanent basis.