The person spoke to The Associated Press on condition of anonymity Thursday because the team hasn't announced its plans.
Stanton signed a $1.25 million, one-year deal last week to be Mark Sanchez's backup, but the Tebow deal has relegated Stanton to another third-string job. He left the Detroit Lions for a chance to be a No. 2 QB after sitting behind Matthew Stafford and Shaun Hill.
New York sent fourth- and sixth-round picks to Denver for Tebow shortly after signing Sanchez to a three-year extension.
Stanton has played in 12 games, including four starts, since being drafted in the second round five years ago.
The Associated Press contributed to this report.