Zaire is expected to graduate in December and will be eligible immediately next season at whichever school he chooses.
Schools Zaire is looking at include Florida, Michigan State, Pitt and Wisconsin, according to a source.
IrishIllustrated.com first reported the news earlier Tuesday.
Zaire won 2014 Music City Bowl MVP honors in his first career start and started the first two games of Notre Dame's 2015 season before sustaining a broken right ankle that ended his season. He worked his way back from injury in time for 2016, and Kelly said in preseason camp that Zaire and DeShone Kizer would both play this fall.
But after Kizer outplayed Zaire in the season-opening loss at Texas, Kizer assumed starting duties for the rest of the season.
Zaire will leave the Fighting Irish with a career 59.2 completion percentage for 816 yards, six touchdowns and zero interceptions. The lefty added 324 rushing yards and two rushing touchdowns. He finished with a 3-0 career record as a starter.