Unger hurt his foot late last season and missed a game at Tampa Bay in December. Payton said Saturday that Unger decided to have surgery to insert a screw into the foot after they didn't see positive results following their initial plan of resting the Lisfranc injury.
Payton said they're comfortable with the timetable and expect Unger can be back participating in August. The Saints consulted with renowned foot expert Dr. Robert Anderson on the injury.
"I see him possibly being able to get into the preseason," Payton said. "Our goal would be Week 3 (of the preseason). So that's where he's at. It wasn't anything new, and yet we were hoping the rest would help it out. ... We're getting ahead of it."
The NFL Network reported earlier this week that Unger would miss the start of the regular season.
Unger, 31, has emerged as one of New Orleans' best and most valuable players since arriving in the Jimmy Graham trade two years ago.
The 6-foot-5, 305-pounder was a two-time Pro Bowler with the Seattle Seahawks and has remained one of the NFL's top centers in New Orleans. He signed a three-year extension worth more than $21 million last summer.
With his combination of power and athleticism, Unger is a key to both the Saints' elite passing game and their revamped rushing attack with Mark Ingram, free-agent signing Adrian Peterson and rookie Alvin Kamara. The Saints have long valued interior offensive linemen as protectors for quarterback Drew Brees, who likes to step up into the middle of the pocket.
New Orleans has a solid backup option at center. Fifth-year veteran Senio Kelemete has started 14 games during the past two years, mostly at guard, and has served as a versatile backup at guard, center and even tackle when needed.
Information from ESPN's Mike Triplett was used in this report.