Payton didn't offer any new insight into negotiations for a possible Butler deal, but he did compliment the defender for his "amazing" story.
"Coming out of a small town in Mississippi and through junior college and into West Alabama, it's pretty amazing," Payton told XTRA 1360 radio in San Diego on Friday. "And the first three years he's had in this league, shoot, he's had a tremendous amount of success, winning two Super Bowls in three years and being a big part of a team that's accomplished a lot.
"So I'd say he's humble, but when you watch the tape, he plays with a chip on his shoulder."
Butler, who is a restricted free agent, visited the Saints on Wednesday and Thursday. The Saints are considering a contract offer for Butler and a possible trade with the Patriots.
"We've practiced with New England now in that three-year time frame twice, so there's a lot of additional practice tape that we have a chance to look closely at," Payton said, referring to joint practices during training camp. "And I'm sure Bill [Belichick] and his staff were the same way when evaluating [receiver Brandin] Cooks."
The Saints traded Cooks to the Patriots on March 10 for the No. 32 pick in the draft and a swap of midround picks. During a radio interview with Mile High Sports in Denver earlier this week, Payton discussed the trade and reiterated that the Saints wanted more assets to help fix their defense.
"I think for us it's improving defensively, and we're looking closely at all of our options to do that," Payton said. "We weren't actively shopping him. A handful of teams had called regarding possibly acquiring him. He's a fantastic guy, someone who worked really, really hard here. We knew coming out of college the makeup was fantastic, and he came in and had a lot of success."
Payton said the trade didn't have anything to do with the emergence of wide receiver Michael Thomas, who caught 92 passes for 1,137 yards as a rookie in 2016.
The coach wasn't specifically asked about how Cooks expressed his frustration with his role in the Saints' offense last year, but he did acknowledge that New Orleans' passing game doesn't focus on one specific receiver.
"Ultimately one of the challenges sometimes, especially here in this offense, is the ball gets spread around some, and yet you're looking at a player that had over 1,200 yards receiving," Payton said, though Cooks finished with 1,173 yards in 2016.
"And it really got down to an opportunity to help improve our team possibly defensively. And we'll be able to look at it three years down the road with what we're able to do with the first-round pick and also the additional third-round pick."