The trade deadline is 4 p.m. ET on Oct. 31.
"Sitting here, everyone knows how I feel. Everyone knows I don't want to get traded," Barkley said Thursday. "I don't think anyone in their right mind would want to get traded anywhere. It's not an easy thing to do. You have to move. I have a family. I would love to be here.
"But like I said, it's not in my control. My focus is to be the leader I can be for this team and get this thing on the right track."
Barkley and the Giants (1-5) host the Washington Commanders on Sunday.
This will be Barkley's second game back after missing three games because of a high ankle sprain. He rushed for 93 yards on 24 carries in Sunday night's 14-9 loss to the Buffalo Bills.
The No. 2 overall pick by the Giants in the 2018 NFL draft has 207 rushing yards and two total touchdowns this season.
The argument can be made for the struggling Giants to start moving players. This season, to date, has been an unmitigated disaster, a surprise on the heels of last season's success when New York reached the postseason and won a playoff game in its first year under general manager Joe Schoen and coach Brian Daboll.
Barkley remained healthy the entire 2022 season and finished with a career-high 1,312 rushing yards. But he was unable to reach agreement on a long-term deal with the Giants and instead settled for an adjusted franchise tag on the first day of training camp that included an extra $1 million available in incentives.
The veteran running back did not partake in the team's offseason workout program this spring as they tried to work out the contract situation.
Barkley is set to become a free agent again at the end of this season. The Giants have the option to use the franchise tag for a second straight year.
This uncertainty gives credence to the idea that moving Barkley at the deadline could be best for the player and the organization. Not that it's something Barkley has considered.
"That never crossed my mind," he said. "Obviously I've been public and vocal about how I feel about this organization and where I want to be. But like I said, knowing the business and seeing that side of it, there are a lot of things that I can't control."
Barkley insists a trade isn't something he has discussed with his personal team. He doesn't believe it's worth his time.
In the meantime, he has other things to capture his attention.
"It's not really blocking it out. I can't control that. It's not like I'm able to make any decisions or have any say in that," Barkley said. "Only say I have is the way I show up to work and the way I go out there and compete. That's the things I can control."