Johnson, who turns 25 on Feb. 16, already is the youngest full-time coach on Utah's staff. He would replace Norm Chow, who served as Utah's coordinator for one year before taking the head job at Hawaii.
Whittingham often cited the 65-year-old Chow's 38 years of experience as a huge benefit to Utah's program.
While Johnson is one of the least experienced coaches on Utah's staff, Whittingham frequently has spoken highly of the former quarterback's feel for the game.
He also has extensive knowledge of the spread offense, a scheme the Utes have indicated they might return to in 2012.
Still, the hiring would be a surprise to many, given Johnson's inexperience and Whittingham had 70-plus applicants for the job.
The applicants included former BYU coach Gary Crowton and Aaron Roderick, Utah's receivers coach who shared co-offensive coordinator duties with Dave Schramm in 2010.
It's unclear how the hiring would affect Roderick's role with the Utes.
Johnson, from Baytown, Texas, went 26-7 as Utah's starting quarterback to set a school record for wins. He was the MVP of the 2007 Poinsettia Bowl and 2009 Sugar Bowl, a victory which completed a 13-0 season for the Utes.