Frazier's interview came one day after Jacksonville Jaguars defensive coordinator Mike Smith had his second meeting with the team.
Smith previously talked with Falcons owner Arthur Blank before Friday's first meeting with the team's new general manager, Thomas Dimitroff.
Frazier, contacted by The Associated Press after Saturday's interview, wouldn't disclose details of the talks.
"Anything going forward would have to come from the Falcons," Frazier said.
A league official who confirmed the interviews with Frazier and Smith said no further interviews are scheduled for Sunday, when the Falcons likely will have great interest in the outcome of the NFC championship game between the New York Giants and Green Bay.
If the Giants lose, the Falcons may again seek an interview with New York defensive coordinator Steve Spagnuolo. They were denied permission to interview him while the Giants are in the playoffs.
Frazier, 48, was a candidate to be head coach in Miami before the Dolphins hired Dallas assistant Tony Sparano, who also interviewed with the Falcons.
When asked if he has been approached by Washington or any other team, Frazier said "There were inquiries by a couple of different teams."
In his first season in Minnesota, the Vikings led the NFL in rushing defense but ranked last in passing defense.
The Vikings led the league with eight defensive scores.
Before moving to Minnesota, Frazier coached defensive backs in Indianapolis for Tony Dungy.
Indianapolis assistant head coach Jim Caldwell, who also has interviewed with the Falcons, has been announced as the successor if Dungy retires.
Among the other defensive coaches to interview with the Falcons are former Baltimore Ravens defensive coordinator Rex Ryan, who has met with the team twice, and Tennessee Titans defensive coordinator Jim Schwartz.
Ravens owner Steve Bisciotti said Ryan, who was fired with head coach Brian Billick, will be asked back on new coach John Harbaugh's staff if Ryan doesn't get hired by Atlanta.
Smith first interviewed with the Falcons before the Jaguars lost to the New England Patriots in a divisional playoff game.
Joining Smith and Ryan as the only candidates believed to have had two interviews with the team is Jason Garrett, who said Thursday he will remain in Dallas as the Cowboys' offensive coordinator.