Players on the PUP list can be removed from the list at any time. Byrd had back surgery in May and did not participate in the team's offseason program.
Saints coach Sean Payton said Byrd will be back "sooner than later."
Byrd signed a six-year, $56 million contract with $28 million guaranteed with the Saints this offseason after spending his first five seasons with the Buffalo Bills.
Saints general manager Mickey Loomis refused to talk about Byrd's condition.
"I don't really want to get into any discussion of that," Loomis said, via the New Orleans Times-Picayune. "We did a physical on him (prior to signing). We felt really good about his physical condition."
- Scooby Axson