The head of the Heisman Trophy Trust said Wednesday that the 2005 award will be vacated.
"We've determined that there will be no winner," William Dockery said in an interview with ESPN.
Bush announced Tuesday that he would forfeit the trophy after the NCAA ruled him ineligible for that season due for receiving improper benefits while he starred for Southern California.
The Heisman Trophy Trust requires players to be in good standing with the NCAA to be eligible for college football's highest honor.
Former Texas quarterback Vince Young finished a distant second to Bush in the voting that year. There was speculation that Young might be given the award if it was taken from Bush.
Dockery said Bush, now with the New Orleans Saints, met in New York last week with some of the eight members of the trust. He did not disclose what was discussed in that meeting, but did say Bush was not given any notice of whether the trust intended to strip the former Southern California star of his trophy.