According to this USA today, Drew Brees told insider Jay Glazer:
“'My problem is next week, when I’m expecting not to have any pain, and actually be able to grip the ball, I have to hold myself back form thinking I’m good to go,' Glazer said via Brees.
Glazer then went on to say, "But [Brees is] really looking at five weeks."
If he misses five weeks, Brees would be back for the team's Oct. 27 game at home against Arizona. It very well could come down to how the Saints are doing through the next few games. The team has a bye in Week 8, and the target return seemed to make sense it would be after the bye week, essentially giving Brees and extra week.