The report suggests Bills chief operating officer Russ Brandon interviewed for Shanahan rather than vice versa.
"We had an excellent meeting," Shanahan told Schefter on Wednesday. "I was really impressed with Russ Brandon and everything he had to say. We're going to stay in touch and see what develops."
The Bills are expected to take their time in making a hire and will interview several more candidates before they find the permanent replacement for Dick Jauron, who was fired last week and replaced with defensive coordinator Perry Fewell on an interim basis.
Almost all of the top-tier candidates have rebuffed the Bills' attempts to talk about the job. Substantive reports have stated Jon Gruden, Bill Cowher and Mike Holmgren have turned them down.
The next wave of candidates might include the likes of Brian Billick, Jim Fassel, Mike Martz and Jim Haslett, but the Bills seem hot for an offensive-minded coach, which could work against Haslett, a former Bills linebacker.
Billick had an 80-64 career record and won a Super Bowl with the Baltimore Ravens. Defense was the foundation of those Ravens teams, but Billick is a lifelong offensive coach who had a star quarterback only once in his nine seasons there. Billick won 13 games with Steve McNair in 2006.
Fassel went 58-53 as head coach of the New York Giants and won an NFC title. Bills fans might note some similarities between their team and the one Fassel took over in 1997. The Giants went 6-10 the year before, but Fassel guided them to a 10-5-1 record and the NFC East championship with Danny Kannel and Dave Brown as his quarterbacks.
Martz coached The Greatest Show on Turf with the St. Louis Rams for six seasons. He went 53-32 and won an NFC title. His offense ranked No. 1 in the NFL in 2000 and 2001 with such stars as Kurt Warner, Torry Holt and Marshall Faulk.
Another offensive-oriented coach who has been mentioned is longtime NFL offensive coordinator Marc Trestman, who has been tearing up the Canadian Football League as head coach of the Montreal Alouettes.
But one major hang-ups the Bills will have is their quarterback situation. They have no obvious starting quarterback on their roster. The organization apparently has given up on Trent Edwards, and Ryan Fitzpatrick isn't held in high regard. Newly acquired third-stringer Brian Brohm is a project.
Many coaches' names will be associated with the opening. Expect some surprises along the way.