A specific reason for Munchak's decision has not been announced, however he could see himself as a candidate for the Steelers' offensive coordinator job should Todd Haley opt to depart.
Munchak followed up a three-year stint as head coach of the Tennessee Titans by spending the last four years with the Steelers. He was a nine-time Pro Bowl selection during his 12-year Hall of Fame playing career.
The 57-year-old Munchak was among several candidates for the Cardinals' job, including Philadelphia Eagles quarterbacks coach John DeFilippo. The Philadelphia Inquirer reported on Tuesday that "as of now" the 39-year-old DeFilippo is expected to interview with Arizona again.
Arizona reportedly also has interviewed its defensive coordinator James Bettcher, Carolina Panthers defensive coordinator Steve Wilks, Minnesota Vikings offensive coordinator Pat Shurmur and New England Patriots defensive coordinator Matt Patricia and linebackers coach Brian Flores.
The Cardinals are seeking a replacement for Bruce Arians, who retired on New Year's Day after five seasons as the team's head coach.
The 65-year-old Arians owned a 49-30-1 mark with the Cardinals and was a two-time NFL Coach of the Year recipient, capturing the honor in 2012 with the Indianapolis Colts and 2014 with the Cardinals.