Instead, Turner will withdraw from SMU and pursue a professional career, Yahoo! Sports reported Tuesday.
Turner is seeking a quicker path to the NBA and hopes to sign with a pro team either overseas or in the NBA Development League next season, according to the report.
"I had to step back and re-evaluate what my main goal and my dream was," Turner told Yahoo! Sports. "My dream is to be a professional athlete in the NBA, and I think this is what's going to bring me closer to it. In college, you get your degree and everything, but going pro is getting me closer to my dream and what I want to do in life."
After a disappointing freshman campaign at Arizona, Turner decided to transfer to SMU, where he would have had to wait until the 2013-14 season to become eligible to play.
SMU currently is transitioning to new membership in the Big East. This spring, the school hired Brown to build the program through that transition. Turner was Brown's first high-profile transfer into the program.
Turner entered Arizona last season ranked No. 3 among point guards, and No. 15 overall, in the class of 2011. But he struggled on and off the court, averaging just 6.8 points and 2.4 assists per game while being suspended twice by Arizona coach Sean Miller. Arizona finished 23-12 but failed to make the NCAA tournament.