However, Russini reported that Peterson is prepared to play at some point this preseason with his new team, which would be a change from years past.
Quarterback Drew Brees and running back Mark Ingram also won't play against the Browns, Russini reported.
Peterson, 32, hasn't played in a preseason game since 2013 and hasn't carried the ball in a preseason game since 2011 with the Minnesota Vikings.
Peterson hasn't said definitively that he will play this preseason, but suggested on Saturday that he's interested in the idea.
"In a sense, I do [find myself more eager to play]. Maybe I'm itching a little more this offseason," said Peterson, who fully participated in the Saints' offseason workout program, OTAs and minicamp -- a change from his years in Minnesota.
Peterson said he doesn't have concerns about his physical ability to be ready for Week 1, with or without preseason action. But he has said he's still getting up to full speed with a new playbook and new system.
"It's more mentally, fully understanding the offense," Peterson said. "Because Drew Brees -- he's a general back there and he talks so fast when he calls plays. So that's more so what I mean, just locking that in. And that's the norm coming into a new system."
Brees, 38, didn't play the preseason opener in 2015 or 2014 (when he was dealing with an oblique injury). But he used to play regularly in preseason openers before that.
The Saints will also likely debut without either of their two first-round draft picks. Cornerback Marshon Lattimore has been sidelined for more than a week with a knee injury that coach Sean Payton described as a tweak. And offensive tackle Ryan Ramczyk has been absent since leaving Saturday's practice early with an unspecified injury.