Byrd was placed on New Orleans' physically unable to perform list on Friday shortly before the opening practice of camp.
Byrd won't be permitted to practice until removed from the list, but coach Sean Payton said 2013 Pro Bowl defensive back is on the verge of being fully fit and will return to practice before camp ends.
''I don't want to put a time on it, but his progress is, I would say, ahead of schedule,'' Saints coach Sean Payton said. ''We're still just getting it to where we feel like it's 100 percent.
''Clearly, before we leave here, he will be back on the roster,'' Payton added. ''It's just a matter of us making sure we feel that he's ready to go at 100 percent and there's no risk of any (further) injury.''
Byrd, who is entering his sixth pro season, signed a six-year, $56 million free-agent contract with New Orleans last March. In May, he had what Payton has described as minor, elective back surgery.
Byrd spent the first five years of his NFL career with the Buffalo Bills, during which he grabbed 22 interceptions and twice led the AFC in that category.
''I was happy,'' third-year safety Kenny Vaccaro said of his reaction to Byrd's signing in March. ''I was saying last year, I was watching his tape in the middle of the year just trying to be like him. It was a surprise, but I'm glad he's here.''
AP NFL website: www.pro32.ap.org and www.twitter.com/AP-NFL