The meeting, the sources said, took place in Indianapolis, where the veteran quarterback played his previous 14 NFL seasons.
Dolphins offensive coordinator Mike Sherman was part of the contingent that met with Manning, the sources said. Sherman was once part of the Texas A&M coaching staff as an assistant who recruited Manning out of Newman High in New Orleans. It was one of the few visits Manning made during the recruiting process in which he chose the University of Tennessee.
Manning still plans to visit with the Tennessee Titans on Tuesday or Wednesday, sources said. Titans coach Mike Munchak will be joined by a select few Titans offensive staff assistants at the meeting. Munchak, a Hall of Fame guard, was a teammate of Manning's father, Archie, during the 1982 and 1983 seasons with the Houston Oilers.
Manning has continued to rehab his shoulder and neck and also will resume his throwing regimen -- most likely at Duke University -- while he analyzes his free-agent choices with no apparent deadline in place to make a decision, a source added.
The Dolphins will continue exploring other options when the new league year begins Tuesday at 4 p.m. ET. Green Bay Packers backup quarterback Matt Flynn is among those options, having played for Philbin when he was the team's offensive coordinator.
The Titans were preparing to make a major run at Houston Texans defensive end Mario Williams, but the organization has shifted its focus to Manning, a league source told ESPN NFL Insider Adam Schefter.
"I want Manning," Titans owner Bud Adams told The Tennessean on Sunday. "I'd love to see him in Titan blue after watching him so many years with the Colts. ... I want him. I am ready to do what it takes to get him aboard, and I think he'd be the guy to get us into the playoffs."
The Titans already have veteran Matt Hasselbeck, signed to a three-year contract last July, and Jake Locker, picked with the No. 8 overall selection in the 2011 draft. But Hasselbeck is due $5.5 million in salary this year after getting a chunk of his deal last season.
Manning on Sunday completed an exhaustive three-day road trip in which he is known to have visited with Denver and Arizona, the two teams that sources believe have emerged as the favorites for the free-agent quarterback.
Despite those sources' contention about the Broncos and Cardinals as favorites, Manning has not engaged either in contract negotiations.
Information from ESPN NFL Insider Adam Schefter and The Associated Press contributed to this report.