The team already has interviewed seven candidates since firing Andy Reid on Dec. 31, and has permission to speak to two other coordinators.
Gruden, the younger brother of Jon Gruden, just finished his second season in Cincinnati. He previously served as an offensive assistant on his brother's staff in Tampa Bay from 2002-08. He also coached several years in the AFL, winning the Arena Bowl title twice.
Gruden interviewed with Arizona on Thursday.
The Eagles are expected to interview Indianapolis offensive coordinator Bruce Arians and Seattle defensive coordinator Gus Bradley.