Quinn missed Cleveland's final two games after hurting his left foot in a Dec. 20 win over Kansas City. The team has not given specifics of Quinn's injury.
But a league source told the The Plain Dealer of Cleveland that Quinn has a Lisfranc injury, and is scheduled to meet with a specialist Tuesday.
Holmgren, who took over the club's football operations last week, said he met with the team's medical staff and was told Quinn needs time for his injury to heal but likely would be able to avoid surgery.
Surgery would require a recovery time of several months. Without an operation, he might be able to resume workouts in less than a month.
Quinn opened the season as Cleveland's starter, was benched after 10 quarters, then got his job back. He went 2-7 in nine starts. He finished 136 of 256 (53 percent) for 1,339 yards with eight touchdowns and seven interceptions.
Information from The Associated Press was used in this report.