Adam Schefter of ESPN provided the update Saturday.
Bryant and New Orleans agreed to a one-year contract Wednesday.
The 30-year-old former longtime Dallas Cowboy made his practice debut with the team Thursday and expressed excitement about the offense's talent.
"Who wouldn't want to play with Drew Brees? Not taking away from nobody else, but you got a guy like Drew Brees, you've got a guy like Michael Thomas, Alvin Kamara, Mark Ingram, you've got those type of guys. Little baby GOATs around here," he told reporters.
Head coach Sean Payton even suggested Bryant might have been ready to play a limited role in Sunday's Week 10 tilt against the Cincinnati Bengals.
Instead, the wideout's season ended before it started.
The eight-month timetable would put Bryant on track to reach full strength by mid-July, right before the start of training camps.
Whether the Oklahoma State product, who'd remained on the free-agent market since Dallas released him in April, will be able to land another contract right away in unclear. Along with proving he's healthy, he may have to wait for injuries to arise if he wants to play in 2019.
The three-time Pro Bowl selection tallied 69 catches for 838 yards and six touchdowns for the Cowboys in 2017.