Yahoo Sports and ESPN reported that Kelly, through his representativeness, reached out to other college football programs. He may also consider opportunities in the NFL, a source told ESPN.
The reports surfaced hours after Notre Dame's season-ending 45-27 loss to USC on Saturday dropped the Fighting Irish's record to 4-8 -- the school's second-worst record of the last 52 years.
"I felt that I was clear with the media following yesterday's game at USC when I was asked about my desire to be back as the head football coach at Notre Dame, but in light of media reports that surfaced afterward, let me restate my position. I have not been, am not, and will not be interested in options outside of Notre Dame," Kelly said in the statement early Sunday morning. "I'm fully committed to leading this program in the future."
The 55-year-old Kelly just completed his seventh season as head coach at Notre Dame, which got news Tuesday that the NCAA ordered the Fighting Irish football team to vacate 21 wins from its 2012 and 2013 seasons in an academic misconduct case involving eight players.
Kelly's seven-year record at Notre Dame is 59-31, with a 12-1 season in 2012 and a 10-win season in 2015. He clinched a bowl berth in each of his first six seasons.
Sources told Yahoo Sports that Kelly's curiosity regarding other jobs was not spurred by the NCAA sanctions and predates that development.
Notre Dame athletic director Jack Swarbrick has consistently stated that Kelly's job is safe.
"Brian will lead this team out of the tunnel opening day next year," Swarbrick told ESPN last month.
At the time, Kelly expressed he was "disappointed" to receive a vote of confidence from Swarbrick.
"Anytime that your athletic director has to come out and say that, as a head coach you're disappointed that any comments like that have to be made," Kelly said at an Oct. 25 press conference. "I didn't ask him. That was his decision, but, you know, I clearly understand what he was doing. He was probably sick and tired of being sick and tired, too. But for me, it's disappointing, you know, certainly that you have to make those comments."
The Fighting Irish finished their worst season since a 3-9 mark in 2007 under Charlie Weis, and their largest margin of defeat this year in the loss to USC.
"Oh yeah, absolutely," Kelly told reporters Saturday when asked if he expected to be back next season. "I thought we could play with anybody this year. We just have not been able to sustain consistent performance for four quarters.
"One side of me says, 'look, this is my 25th year, I know what I'm doing.' But on the other side of it, you can't be surprised that when you go 4-8, that you're going to get those questions asked as well.''