ESPN also reported the Colts requested to meet with New England Patriots offensive coordinator Josh McDaniels.
Carolina Panthers defensive coordinator Steve Wilks, who is a first-year coordinator, also was requested by the team for an interview.
Colts GM Chris Ballard said Monday that previous head-coaching experience is not a requirement for the job. Pagano also did not possess any experience as a head coach when the Colts hired him on Jan. 25, 2012.
Vrabel, 42, is a three-time Super Bowl champion with the Patriots and also played with the Pittsburgh Steelers and Kansas City Chiefs.
Since retiring as a player in 2011, Vrabel spent three seasons as a linebackers and defensive line coach for Ohio State, then three seasons as Houston's linebackers coach before being elevated to defensive coordinator this season.
The Detroit Lions also requested to interview Vrabel, whose name also came up last season when the Los Angeles Rams were searching for a new coach.
McDaniels also was requested by the New York Giants, Arizona Cardinals and Detroit.
McDaniels was fired during his second season as head coach with the Denver Broncos, with whom he posted an 11-17 mark during the 2009-10 seasons. The 41-year-old is in his 14th overall season with the Patriots.
McDaniels was asked Monday how he will balance requests by teams seeking permission for interviews with preparing for the Patriots' next opponent.
"Yeah, I mean, that process -- whatever it is -- it will take place. I mean, I'm certainly not aware of anything at this point," McDaniels said. "I've just been focused on trying to grade our tape and work with our staff to try to get ourselves ready to have a productive week here with our guys and get ready to go.
Wilks also is being sought after by the Lions and Giants, but he remains focused on preparing for Carolina's playoff game against New Orleans.
"That's what you work hard for," Wilks said. "But most importantly, trying to stay focused on the Saints."
Wilks cannot meet with teams until Carolina is finished in the postseason. Wilks also interviewed last offseason for the Rams' vacancy that ultimately went to Sean McVay and took over as Carolina's defensive coordinator when Sean McDermott was hired to coach the Buffalo Bills.
The Panthers ranked third in rushing defense (88.1 yards per game), third in sacks (50) and seventh in total defense (317.1).
Wilks spent five seasons as Carolina's defensive backs coach and has been the team's assistant head coach in the last three seasons.
Before coming to Carolina, he spent three seasons apiece as the defensive backs coach of the Chicago Bears and San Diego Chargers.