The Miami Herald, citing an unnamed source close to Bush, reported Sunday that the running back will not return to the team next season.
Three teams contacted Bush once the NFL's three-day negotiating period opened Saturday at midnight but the Dolphins haven't shown any interest in retaining him, the source told the newspaper.
The 28-year-old Bush proved that he can be an every-down tailback in Miami, rushing for 2,072 yards and 12 touchdowns in two seasons with the Dolphins.
In 2012, Bush played in every game for the first time since 2006 and fell just shy of his second consecutive 1,000-yard rushing season, finishing with 986.
In 91 career games, Bush has 4,162 yards rushing and 2,730 receiving with 48 touchdowns (29 rush, 15 receiving, four return).
Information from ESPN.com AFC East blogger James Walker and The Associated Press was used in this report.