Sources told ESPN's Chris Mortensen and Adam Schefter that the Dolphins were informed in no uncertain terms that Manning will not sign with them.
The Dolphins, though, have emerged as the favorites to sign Flynn, league sources have told Schefter.
Flynn visited Miami on Saturday 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.
The Dolphins are looking for an upgrade over incumbent quarterback Matt Moore. Chad Henne, who started 31 games for Miami over the past three seasons, signed Wednesday with the Jacksonville Jaguars as a backup.
Information from ESPN senior NFL analyst Chris Mortensen, ESPN NFL Insider Adam Schefter and The Associated Press was used in this report.