Per Darren Urban of AZCardinals.com, Kingsbury said Tuesday that Josh Rosen is "our guy" when asked about Murray.
Kingsbury inadvertently opened himself up to questions about Murray because of comments he made about the 2018 Heisman Trophy winner last October.
"Kyler is a freak...I would take him with the first pick of the draft if I could," Kingsbury told reporters leading up to a Nov. 3 game between Texas Tech and Oklahoma.
The Cardinals, who own the top pick in this year's draft, hired Kingsbury on Jan. 8 after he was fired by Texas Tech and signed on to be the next offensive coordinator at USC.
Rosen was Arizona's top draft pick last year (No. 10 overall). The 22-year-old struggled through his rookie season, finishing with 2,278 yards, 11 touchdowns, 14 interceptions and a 55.2 completion percentage.
Until the Cardinals make their pick on Apr. 25, Kingsbury will likely have to deflect questions about Murray to avoid potentially alienating his current quarterback in the developing stages of his career.