A day after his interview, coach Brian Daboll and General Manager Joe Schoen approached him before the start of practice.
"Yeah, [a trade] is not happening," Daboll told Barkley, via Jordan Raanan of ESPN.
The Giants are only 2-5 and could look to sell before Tuesday's trade deadline.
It is unclear if Barkley even would have anyone interested in him, considering his salary and the fact that he's scheduled to become a free agent in 2024, and the Giants likely would get little in return if a team was interested.
"I don't think it made me feel any better or any worse," Barkley told ESPN of his conversation with Daboll and Schoen. "It wasn’t like I was too overly concerned about it, to be honest. And I never even thought about it until the question was brought up. I didn't even realize when the trade deadline was."
The franchise tag was $10.1 million, but Barkley is playing under an adjusted franchise tag that includes a $2 million signing bonus and $1 million in difficult-to-reach incentives.
The sides can reopen negotiations after the season on a long-term deal after not coming to terms before the July 17 deadline. He hopes they can work things out to keep him on the team.
"I want to create a legacy, and the way you do that is by continuing to stay with a team through your whole career," Barkley said. "As I see the NFL and realize the business, you know, it's less likely for that to happen for players. But if you're able to accomplish that, it's special."