Drew Brees lost his blindside protector Jermon Bushrod to the Bears, who made him the highest-paid offensive lineman in franchise history.
In related news, the Saints are bringing in Oklahoma tackle Lane Johnson for a visit Tuesday, according to the Chicago Sun-Times.
The Saints would have to trade up to get any of the top three tackles: Luke Joeckel, Eric Fisher and Johnson.
Coach Sean Payton said finding a left tackle and improving the pass rush are the two areas that keep him up at night.
Payton said Charles Brown, a 2010 second-rounder, could play left tackle if he stays healthy.
"He has to be available," Payton said last month. "Year after year, if you're unable to (remain healthy enough to play), then it becomes as a coach, 'Do we have him? Do we not have him? ... It's hard to gameplan then.
"I look at that spot like there's a magnet with no name on it," he added. "Gray, it's just gray."