Pelissero mentions that it was going to be too difficult for Bryant to be ready to go after just two days of practice and the Saints would like to have him lose five pounds and get back into football shape while their offense.
According to Pelissero, Bryant could make his debut the following week against the Eagles.
Bryant, 29, is a former first-round pick of the Cowboys back in 2010. He was in the third year of his five-year, $70 million contract that included $45 million guaranteed and was set to make base salaries of $12.5 million over the final two years of the agreement when Dallas released him in a move that freed up $8.5 million of available cap space.
The Saints signed Bryant to a one-year deal worth $600,000 over the remainder of the season.
In 2017, Bryant appeared in 15 games for the Cowboys and has caught 66 passes for 814 yards receiving and six touchdowns. Pro Football Focus had him rated as the No. 45 receiver out of 116 qualifying players.