"I don't see that being a long, drawn-out process, and I think we've been here before," Payton said at the NFL Combine on Thursday, per the Times-Picayune of New Orleans. "I think that's going to get done fairly smoothly."
Payton said Saints general manager Mickey Loomis already has met with Brees and also is expected to sit down with the quarterback's agent, Tom Condon, this week.
Brees signed a five-year contract extension worth an average of $24.5 million per season that can be voided on March 14, making the 39-year-old an unrestricted free agent as the team carries a cap hit of $6 million and dead cap value to $18 million.
"There's no assumptions, but I'm fairly confident," said Payton. "It's not something I've been focused on a lot."
A former Super Bowl MVP and 11-time Pro Bowl selection, Brees has said he wants to remain with New Orleans. He told ESPN before the Pro Bowl in January that he's "not going anywhere else."
Brees completed a career-high 72.0 percent of his passes for 4,334 yards and 23 touchdowns while leading the Saints to an 11-5 regular-season mark. The touchdown total, however, was his fewest since 2007.
He led the Saints to a 24-23 lead over Minnesota with 25 seconds left in the NFC divisional-round playoff game before the Vikings scored the winning touchdown on a 61-yard pass play with no time left.
A second-round selection in the 2001 NFL Draft of the then-San Diego Chargers, Brees has thrown for 70,445 yards with 488 touchdown passes and 228 interceptions in 248 career contests.