Per NFL Network's Ian Rapoport, Jackson interviewed with the Cardinals on Friday for their offensive coordinator position.
Jackson was a candidate for the Cincinnati Bengals' head coaching position after they parted ways with Marvin Lewis.
During his introductory press conference with the Cardinals, Kingsbury told reporters he is going to call the plays on offense and wants his coordinator to help with the game-planning.
"I think the offensive coordinator will be somebody who will come in and help me mesh some of my ideas with some traditional things that they've done in the NFL, be a great leader of men and be able to handle a room, help me install different things," Kingsbury said.
Jackson previously served as offensive coordinator for the Washington Redskins (2003), Atlanta Falcons (2007), Oakland Raiders (2010) and Bengals (2014-15). He was named the Pro Football Writers NFL Assistant Coach of the Year in 2015.
Prior to joining the Bengals' staff last season, Jackson went 3-36-1 in two-plus seasons as head coach of the Cleveland Browns.