Bush currently doesn't have possession of the trophy, having loaned it to the San Diego Hall of Champions in March. NFL Network spoke Thursday with a museum official, who confirmed the statue remains in its possession.
"As of late, we've been working with the family toward the next step for the trophy," said Angela LaChica, vice president of the facility.
LaChica said Bush hasn't made a formal request to take back the trophy, which goes to college football's most outstanding player, as voted on by a panel of sports journalists and past winners.
"The status of the trophy has not changed," LaChica said. "It's still in our possession, and myself, along with my team, are working toward a solution with the Bush family."
A source close to Bush told SportsByBrooks.com on Wednesday that Bush, his stepfather and mother ran into LaChica at a recent event in San Diego, but no plans were put in place to transfer ownership of the trophy. The same source said Bush has decided he will not return the statue to the Heisman Trophy Trust.
According to the website's source, Bush and his parents, stepfather Lamar Griffin and mother Denise Griffin, "loaned" the trophy to the San Diego Hall of Champions with the hope they would quietly regain possession of the bronze statue once the controversy died down.
Bush and USC each received Heisman statues after the running back won the award. USC, which received harsh NCAA sanctions because of infractions allegedly committed by Bush, has since returned its copy to the Heisman Trophy Trust.
A producer for the "Dan Patrick Show" reported earlier in June that the Heisman Trophy Trust had "repeatedly" contacted Bush's agent in an effort to get the trophy. A Heisman Trust source told the producer, "The whole world reasonably expected him to return it."