Casey, whose current contract expires, has agreed to a new three-year deal, according to the reports.
Casey helped guide the Raptors to a 48-win season and their first playoff berth in six years. Toronto fell to Brooklyn in seven games, losing the final contest by one point at home on Sunday.
Toronto has posted a 105-125 regular season record overall since Casey succeeded Jay Triano in 2011.
The 57-year-old previously coached Minnesota and also served as assistant coach with Dallas and Seattle.
He played for the University of Kentucky, winning a national title with the Wildcats in 1978.
Casey was already scheduled to meet with the media Tuesday morning, as is Raptors general manager Masai Ujiri.