General manager Mickey Loomis would be open to trading Payton to another team, sources told the New Orleans Times-Picayune.
The subject of Payton's coaching future was discussed when he met with Loomis following the Saints' 38-32 loss to the Atlanta Falcons on Sunday, a source told ESPN. The Saints finished 7-9 for the third straight season.
Discussions between Payton and Loomis are expected to continue into the week.
Payton, who has been coach of the Saints since 2006, refused to discuss reports about his coaching future following Sunday's loss in Atlanta, saying only, "Next question."
Reports of Payton's possible interest in going to Los Angeles after the Rams fired Jeff Fisher on Dec. 12.
Saints quarterback Drew Brees said he would be surprised If Payton decided to leave.
"I mean, I have no reason to believe otherwise. Sean Payton's our head coach," Brees said after Sunday's game. "And honestly, I don't know where you guys are getting this stuff. I guess there's speculation, whatever. I guess anybody can just write whatever they want, and all of a sudden, people think that it's fact or there's some truth to it. I think it's completely made up, to be honest with you. Coach Payton's our head coach, and that's that."