White was slowed down with ankle and hamstring injuries and Jones also went through a tough 2013 season, missing the final 11 games because of a foot injury.
White, 32, had his lowest receiving yards total since 2006 and had a career-low 11.3 yards per catch.
Atlanta went 4-12 last season, a year after recording a 13-3 mark and losing in the NFC Championship game.
"When you step on the field, you should feel that you're the best, you and whoever your partner is," Jones said, via ESPN.com. "I feel like me and Roddy, we're the best when we step on the field. We take it as a challenge every year: We want to go out and show everybody we're the best one-two in the league."
"Numbers don't lie: They did a good job last year," White said of Marshall and Jeffery. "We weren't there to play in the party. But this year, we're going to be there to play in the party. So at the end of the season, we'll come together, and then we'll see what happens.