ESPN's Dan Graziano cited a source as saying the Broncos (3-7) will make the official announcement Wednesday.
Denver has been plagued by quarterback play during its six-game losing skid. The Broncos fired offensive coordinator Mike McCoy on Monday and promoted Bill Musgrave to the same position.
Lynch, who is a team's first-round pick in the 2016 draft, is now healthy after battling a shoulder injury he sustained during a preseason game against the Green Bay Packers on Aug. 26.
Lynch returned to practice three weeks ago and served as the No. 2 quarterback in practice last week. He was the backup to Brock Osweiler in Sunday's 20-17 loss to the Cincinnati Bengals while fellow quarterback Trevor Siemian was inactive.
Lynch completed 49 of 83 passes for 497 yards with two touchdowns and one interception in three games last season.