The meetings are scheduled to be away from the teams' facilities.
Manning, a free agent, definitely will not be choosing a team by 4 p.m. Tuesday, the commencement of the new league year.
His meeting with Philbin, the Dolphins' new coach, likely will be Monday night or Tuesday morning. His meeting with Munchak is expected to take place no later than Wednesday.
Philbin will be accompanied by Dolphins offensive coordinator Mike Sherman and perhaps other staff members, including general manager Jeff Ireland. 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.
Munchak also will be joined by a select few Titans offensive staff assistants. Munchak, a Hall of Fame guard, was a teammate of Manning's father, Archie, during the 1982 and 1983 seasons with the Houston Oilers.
Besides starring at Tennessee, Manning's wife is from Memphis. He also already knows the Titans' facility a bit, having practiced against Tennessee a few years ago when the Colts came to town for some joint practices.
The discussions are expected to be heavily focused on both teams' football concepts, schemes and personnel.
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 the Denver Broncos and Arizona Cardinals, 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.
In all, 12 teams contacted Manning after he was released by the Indianapolis Colts last week but not all of the teams have been publicly identified.
Information from ESPN NFL Insider Adam Schefter and The Associated Press contributed to this report.