The Colts also have been mentioned as a possible suitor for Payton, according to league sources.
Payton has two years remaining on his contract after this season, but it will not deter teams from approaching the Saints about a potential deal.
There is no indication whether the Saints or Payton would entertain such conversations.
Payton's name has come up in speculation about other jobs over the past year because he has been in New Orleans for 10 years, and the Saints appear to be in a rebuilding mode after overhauling half of their roster.
However, Payton has downplayed rumors linking him to other job openings on multiple occasions.
Payton has ties to current Dolphins interim coach Dan Campbell, who was promoted Monday after Miami fired Joe Philbin. Campbell played tight end for the Cowboys when Payton was Dallas' offensive coordinator and ended his playing career under Payton in New Orleans.
The Saints went 7-9 last year -- Payton's first losing season since 2007 -- and are 1-3 this season entering Sunday's game against the Eagles.
Payton, 51, is 81-51 in his eight-plus seasons with New Orleans.
ESPN.com Saints reporter Mike Triplett contributed to this report.