Meredith has been away from a number of practices and sat out last week's preseason opener, but the injury is not related to the torn ACL that caused him to miss the entire 2017 season, according to the NFL Network.
On Sunday, New Orleans coach Sean Payton cited Meredith as one of a number of injured players who "are coming along well."
Meredith, who agreed to a two-year contract worth an estimated $10 million with the Saints in April, referenced his situation in a Twitter posting on Tuesday.
"So many obstacles on my path, trying to test my perseverance," wrote Meredith, who added that his faith remains unshaken.
A former undrafted free agent out of Illinois State, Meredith had a nondescript first year with Chicago in 2015, when he had only 11 catches for 120 yards.
Meredith had a breakout season in 2016, recording 66 receptions for 888 yards and four touchdowns, and was poised to be an integral part of the Bears' wide receiving corps in 2017 before suffering the knee injury.