Jones, 27, started 13 games at center and left guard last season. He was in a position battle with Jon Halapio, who will now be the full-time starter at center.
"I think that for me," Jones told Matt Lombardo of NJ Advance Media in minicamp, "each and every year has always been a competition to be on the team. It's no different this year. I'm excited for the fall. I'm just trying to improve each day, day-by-day. I want to get better as a football player. I think that's what Jon's trying to do, too. We're both good football players and excited for what the fall brings."
The Vikings will likely start Jones at center, filling one of the biggest needs on their roster. Cornelius Edison handled the duties throughout the preseason because of injuries at the position. Pat Elflein has missed the entire preseason, and Nick Easton is out for the year.
Jones began his career with the CFL's Calgary Stampeders before coming to the Giants in 2015. He's currently playing on a one-year contract after the Giants gave him a second-round tender in free agency this spring.