Taggart has a big-name proponent in his corner in former NFL coach Tony Dungy, who said he spoke to Oregon officials on Taggart's behalf. Dungy's son, Eric, played at Oregon from 2010-13 before transferring to USF for his final season in 2014.
"I certainly think he's a good fit," Dungy said. "I had a chance to watch him coach a year when my son played there. I liked his style. I think he's a guy that can relate to the players very well.
"He's put together two winning programs (at Western Kentucky and USF). He knows the West Coast, having been (an assistant) at Stanford (from 2007-09). He has all the elements Oregon is looking for. He's a bright, young coach and it makes him easy to recommend."
Taggart, in his fourth year at USF, has increased the Bulls' win total from 2 to 4 to 8 to this year's 10-2 record, marking the best record in school history.
"Oregon is a different situation," Dungy said. "You're not coming in taking something from the ground floor. You need a coach that can come in and get players going and coach well. It's a big challenge at Oregon, one that he would be successful at. You're not trying to become respectable, you're trying to win national championships -- it's a different kind of challenge."
Dungy, who lives in Tampa, said it would be bittersweet if Taggart ended up at Oregon.
"Oregon is a great job and hopefully he gets it," Dungy said. "If not, we're happy to still have him in Tampa."
Mullens, as a member of the College Football Playoff selection committee, is in Grapevine, Texas, this weekend.
Mullens also interviewed Harsin, who is 38-13 in four seasons as a head coach: 2013 at Arkansas State and the past three seasons at Boise State.
The Ducks are expected to interview other candidates in the school's search for a replacement for former coach Mark Helfrich, a source said. Among the possible candidates include Western Michigan coach P.J. Fleck, Florida coach Jim McElwain, Ohio State defensive coordinator Greg Schiano and Oakland Raiders offensive coordinator Bill Musgrave, who played quarterback at Oregon.
Oregon has not yet reached out to Fleck, sources said, although there could be some movement Sunday.
The Ducks would prefer to have a new coach in place by early next week, a source said.
ESPN's Adam Rittenberg contributed to this report.