The person spoke to The Associated Press Wednesday on condition of anonymity because the roster move has not been announced.
The mercurial yet prolific wide receiver, who turned 30 on Sunday, had been on the open market since April, when he was released after an eight-season stint with the Dallas Cowboys.
However, Bryant's professional reputation has been marred at times by public confrontations with coaches and teammates during games and practices.
Bryant worked out for the Saints along with Brandon Marshall and Kamara Aiken earlier in the week but left New Orleans without a contract. He'd previously met with Cleveland and Baltimore. But things have been more hit-and-miss behind Thomas, with Ted Ginn (knee) out for the season while Tre'Quan Smith contributes some and Cameron Meredith has now gone catchless in three straight games.
Led by record-setting quarterback Drew Brees, the Saints rank seventh on offense overall, averaging 402.2 yards per game, and seventh in passing, averaging 289.9 yards. The fresh start has helped, as the 27-year-old has 22 catches for 396 yards with two touchdowns in six games with New England.
As for Bryant, one thing he might want to do before his return to Dallas on November 29 is purchase a few extra jerseys, because apparently, a bunch of his old teammates are hoping to trade with him after the game.
New Orleans knew it couldn't go deep in the playoffs without shoring up their defense backfield, hence the trade for Apple ahead of the deadline two weeks ago. The Saints aren't getting the alpha dog receiver we saw in Dallas for seven seasons, but Sean Payton knows that and will craft a role that will allow Bryant to thrive. "He's a good player".