A source told NFL Network and the Boston Globe on Monday that the NFC North franchise requested permission to interview McDaniels and Patriots linebackers coach/defensive play-caller Brian Flores for the role.
The Cleveland Browns also asked for permission to interview Flores.
McDaniels agreed last offseason to become the next coach of the Indianapolis Colts, before turning down the job at the last minute. He has also been linked to the Green Bay Packers opening at head coach.
The 42-year-old has been the Patriots' offensive coordinator for 10 seasons. He posted an 11-17 record in two seasons as coach of the Denver Broncos in 2009 and 2010. McDaniels also served as the St. Louis Rams' offensive coordinator in 2011.
Sources told NFL Network in September that the Patriots were able to hold onto McDaniels this offseason by giving him a five-year contract extension with the franchise.