Pelissero adds that Bryant has been close to a deal before, but all signs pointing toward this deal getting done.
Bryant actually had his own private workout for the Saints on Tuesday.
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.
In 2017, Bryant has 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.
We have him featured in our Top 50 Available 2018 NFL Free Agents list.