"I think both of them have different traits and we need to find a way to win the game and I think both of them can help us win," said Kelly, who has not named a starter for the Dec. 30 contest in Nashville, Tennessee.
Golson, a redshirt junior, started all 12 games for the 7-5 Fighting Irish this season but was replaced by Zaire, a redshirt freshman, in the regular-season finale at USC, a 49-14 loss.
Zaire completed 9 of 20 passes in that game for 170 yards, adding 18 rushing yards and a touchdown on six carries.
Kelly said he would play both next year, too, if it's what's best for the team.
Golson, who was the starter on the Notre Dame team that lost in the BCS title game at the end of the 2012 season, returned in 2014 from a season-long academic suspension and completed more than 60 percent of his passes for 3,355 yards with 29 touchdowns while adding 277 rushing yards and eight more scores on the ground.
But Golson turned the ball over 22 times this season (14 interceptions, eight lost fumbles), with all of them coming during the season's final nine games.
The Irish raced to a 6-0 start and a No. 5 ranking this season before dropping five of their last six games, including their final four.
Kelly also said Monday that safety Eilar Hardy is eligible to play in the bowl game and will graduate following the spring semester.
Hardy was among five players Notre Dame suspended before the season as part of its internal academic probe, and the only one who returned this season.
The redshirt junior safety was cleared before the Irish's Nov. 8 game at Arizona State and played in Notre Dame's final four games this season, mostly on special teams.