Fedora led Southern Miss to an upset of previously undefeated Houston in the Conference USA championship game. The Golden Eagles finished the season 11-2 and will play Nevada in the Sheraton Hawaii Bowl on Dec. 24.
North Carolina (7-5) plays Missouri in the AdvoCare V100 Independence Bowl two days later.
Fedora was 33-19 at Southern Miss, his first head coaching job after assistant coaching positions at Florida and Oklahoma State.
North Carolina's board of trustees has scheduled "emergency meetings to discuss a personnel matter" for Thursday and Friday morning. The school said the board is expected to "take action" during Friday's meeting, with at least some portion of those meetings to be conducted in closed session.
Any deal to hire Fedora would be subject to approval by the trustees, meaning North Carolina couldn't hold a news conference to introduce him until Friday at the earliest.
The Tar Heels were looking for a permanent coach to replace Butch Davis, who was fired shortly before training camp amid an NCAA investigation into improper benefits and academic misconduct within the program. The school then promoted defensive coordinator Everett Withers to interim coach.
Withers led the team to a 5-1 start, though the Tar Heels stumbled down the stretch by losing four of six.
Withers said Monday that he interviewed for the job last week. He said he wouldn't let the uncertainty about his future be a distraction for the Tar Heels as they prepare for a fourth straight bowl game.
He also said he planned to coach the bowl game regardless of his status.
Information from ESPN college football reporter Joe Schad and The Associated Press was used in this report.