"We still have a lot of work to do and I owe this to the players, coaches and this entire organization!" Bieniemy said in a text message.
Colorado athletic director Mike Bohn denied Thursday that he already had offered the job to Embree and told The Associated Press he hoped to hire a football coach in the next few days.
Colorado fired coach Dan Hawkins on Nov. 9 after he went 19-39 in four-plus seasons. He was dismissed three days after the Buffaloes blew a 28-point lead at Kansas with 11 minutes to play, the biggest collapse in the program's 121-year history.
Longtime assistant Brian Cabral took over on an interim basis and went 2-1 as the Buffaloes finished 5-7, their fifth consecutive losing season.
The Associated Press contributed to this report.