ESPN said health and family concerns are at the heart of his decision.
The 7-foot-6 inch Bradley was hampered by knee and hip injuries last season, when he averaged just 2.7 points and almost three rebounds per contest while playing in 77 games.
The ESPN report said Bradley, who was the second overall pick by Philadelphia in the 1993 draft, is trying to negotiate a buyout of the remainder of his contract, which has three years left for $14.5 million.
Bradley, who also has played for New Jersey, spent the last eight and a half seasons with the Mavericks. He has career averages of 8.1 points and 6.3 rebounds in 832 games and led the league in blocked shots twice.
Bradley's playing time was almost non-existent under new coach Avery Johnson. He played a total of 27 minutes in the Mavericks' 13 playoff games.