The Texans, who finished 3-13-1 and fired former coach Lovie Smith last week, completed an interview Monday night with Payton.
Earlier in the day, Payton said on "The Herd with Colin Cowherd" that he was to meet this week with Houston, the Denver Broncos and Carolina Panthers. Sources told ESPN's Adam Schefter that the Broncos interview will take place Tuesday in Los Angeles, and the Panthers meeting is set for Friday.
The Arizona Cardinals also have requested permission from the Saints to meet with the 59-year-old coach, who won the Super Bowl with New Orleans at the end of the 2009 season.
Any team that hires Payton would have to compensate New Orleans, which has rights to the coach through the end of the 2024 season after he stepped away from the job following the 2021 season with three years left on a five-year contract.
Payton said he and Saints general manager Mickey Loomis already have discussed what that compensation potentially would be.
"Ultimately, the compensation for the Saints would be a mid- or late-first-round pick,'' Payton said. "Each team has different ammo or different pick selections. It could be a future one where maybe you have to throw in something.''
Houston has the second pick, Arizona the third, Carolina the ninth and Denver currently the 29th via a trade with San Francisco, which is still in the playoffs.
Asked specifically if he would consider Houston, which has gone a combined 11-38-1 the past three seasons and doesn't have a franchise quarterback, Payton didn't hesitate to say yes.
He noted his knowledge of the organization and key individuals such as general manager Nick Caserio after practicing against the Texans multiple times during his time in New Orleans.
"When you practice for three days with an opponent, you get a chance to meet a lot of the different personalities and people involved in the building,'' said Payton, who has spent this season working as an NFL analyst for Fox Sports. "They've got really good draft capital, really good draft capital. They're in a division that you can at least say with Indy, Tennessee and Jacksonville [is winnable].
"There's growth potential immediately there from their two or three wins they had this year.''
The Panthers on Sunday became the last of the four teams to request an interview with Payton. They already have interviewed former Broncos coach Vic Fangio for their defensive coordinator position and have requested an interview with New Orleans defensive backs coach Kris Richard for the same job.
Fangio, the original defensive coordinator for the Panthers in 1995, has been linked to being a candidate for defensive coordinator under Payton. Richard was Payton's secondary coach in 2021.
Carolina general manager Scott Fitterer also has ties to Richard from their time together in Seattle.
Payton, who had a record of 152-89 in 15 seasons with the Saints, didn't put a timetable on when he could be hired. He reminded that whatever happens, a deal must be worked out between that team and New Orleans.
The first step is getting to know his potential suitors.
"That's the significance of the upcoming week or two, meeting some of these individuals, asking some questions, maybe some difficult questions,'' Payton said. "And trying to get answers so we're not having difficult questions when you've already taken the job."