Barnett, who took Northwestern from the depths of college football to the Rose Bowl last season, told Notre Dame officials he no longer wanted to be considered as Lou Holtz's successor.
Holtz announced his resignation Tuesday and later that day Barnett said he had been contacted by Notre Dame about the job. Reports said he was the leading candidate for one of college football's most prestigious positions.
"I am very humbled and flattered that Notre Dame has asked me to be considered a candidate for their head coaching football position," Barnett said in a statement.
"However, for very personal and private reasons, I have informed Notre Dame officials that I wish not to be considered as a candidate. Regardless of the rumors, an offer was never extended to me by Notre Dame. This is all I will say about this matter."