Mike Zimmer is a long time NFL coach, working in the league since 1994 when he was hired by the Dallas Cowboys as a defensive backs coach. Zimmer was the Cowboys' defensive coordinator from 2000 to 2006 before taking the same job with the Atlanta Falcons. He left for Cincinnati a year later and has been with team since.
The Bengals' defense has excelled under Zimmer, finishing sixth in total defense in 2012 and improving to third overall in 2013. Zimmer won the 2009 NFL Assistant Coach of the Year award.
Gruden has never been a head coach at the NFL level, but did hold head coaching positions in the Arena and United Football Leagues. He's been the Bengals offensive coordinator since 2011. Gruden also worked as an offensive assistant on his brother Jon Gruden's staff at the Tampa Bay Buccaneers. The Bengals' offense had its best season under Gruden in 2013, finishing 10th in the NFL in total offense.
The Bengals face the San Diego Chargers on Sunday in the NFL playoffs, so until their season concludes, the Vikings won't be able to contact either coach.