Manning telephoned the Dolphins on Thursday to advise them he would sign elsewhere, and the team began courting free-agent Flynn, two people familiar with the negotiations said.
Both people confirmed the developments to The Associated Press on condition of anonymity because the Dolphins haven't commented publicly on their free-agent shopping.
Flynn was scheduled to visit Miami by the weekend after concluding a visit with the Seattle Seahawks.
The Dolphins made Manning their top offseason priority and met with the four-time NFL MVP for several hours Monday in Indianapolis, but Flynn had long been considered a potential fallback. He was a backup the past four years for Green Bay, where he worked with new Dolphins head coach Joe Philbin, who was previously the Packers' offensive coordinator.
Flynn was a seventh-round draft pick by the Packers in 2008 after playing at Louisiana State. He has only two career NFL starts, but one was an eye-catching performance in last year's regular-season finale, when he set franchise records with 480 yards passing and six touchdowns to help the Packers beat Detroit 45-41.