The Chiefs already have started their head coaching search and have had "several interviews," a Kansas City source told Schefter.
Those interviews took place before the end of the season, but the source declined to identify any of those candidates. Philbin also is on the Miami Dolphins' list of candidates to interview.
Romeo Crennel went 2-1 as interim coach following the dismissal of Todd Haley, making a strong case to be hired on a permanent basis. The two victories were over division champions Denver and Green Bay -- the Packers' only loss this season -- while the lone loss came in overtime.
General manager Scott Pioli has said Crennel will be interviewed for the full-time job, though it's unclear when that will happen.
A source told ESPN.com's Bill Williamson that Crennel is expected to interview for the Chiefs job in the next several days.
Crennel, the former Cleveland Browns head coach, said he'll listen to other opportunities "at the appropriate time," even if they're outside of Kansas City.
The Chiefs ended up 7-9 during a roller-coaster year that included plenty of highs -- a four-game winning streak, the only victory over the Green Bay Packers -- and stomach-churning lows, such as two defeats by a combined 89-10 to start the season, and the firing of Haley after a penalty-filled 37-10 loss to the New York Jets in which he earned his own unsportsmanlike conduct flag.
Injuries decimated the Chiefs, starting in the preseason when tight end Tony Moeaki tore the ACL in his left knee, forcing him to have surgery and spend the past four months doing grueling rehab work.
Pro Bowl safety Eric Berry went down with the exact same injury during the Chiefs' season-opening loss to Buffalo, and All-Pro running back Jamaal Charles followed suit in Week 2 at Detroit -- three of the team's brightest young stars undergoing rehabilitation while the team pressed on without them.
Information from ESPN NFL Insider Adam Schefter, AFC West blogger Bill Williamson and The Associated Press was used in this report.