Heaps declined to comment when reached Monday, but indicated he would speak about his decision at a later time.
Heaps started the last 10 games of his freshman season, and the first five games in 2011 before being replaced by junior Riley Nelson.
After Nelson was injured against Idaho, Heaps entered the game and played well against the Vandals. He started against New Mexico State and led the Cougars to a 42-7 win, but Nelson regained the starting position Saturday against Hawaii, when he returned from the injuries suffered against Idaho.
In high school, Heaps was rated as the No. 1 quarterback prospect in the country by Scout.com. He was named a Parade All-American following his senior season and started in the U.S. Army All-American Bowl after leading Skyline to consecutive championships.
Heaps' signing with BYU was a major media event, with the quarterback introduced at a downtown Salt Lake City restaurant during a ceremonial signing event, along with several other Cougar recruits.
Expectations soared after he set school freshman passing records for yards, touchdowns and wins and became the first-ever BYU true freshman to win a bowl game. Heaps was the MVP of the 2010 New Mexico Bowl after passing for 264 yards and four touchdowns.
He completed 363 of 635 passes for 3,768 yards and 24 touchdowns in his BYU career.
The school has granted Heaps a release to transfer, but said he will not participate in the Armed Forces Bowl on Dec. 30 against Tulsa or in any practices leading up to the game.
Heaps has not announced his intentions of where he will transfer, though Washington, Washington State, USC and California are believed to be on his short list.
Heaps' highlights and lowlights
• Set school freshman passing records for yards, touchdowns and wins
• Threw 14 touchdowns in final six games of the season
• Earned MVP honor in New Mexico Bowl in win over UTEP
• Started first five games but struggled, throwing five interceptions and only three touchdowns
• Lost starting job to Nelson after falling behind against Utah State
• Regained starting role after Nelson was injured, threw six touchdowns in two games
• Relegated again to backup after Nelson returned in win over Hawaii