Turkoglu, whom the Toronto Raptors dealt to the Suns for Leandro Barbosa and Dwayne Jones, was in Turkey practicing with his country's national team for the upcoming World Championships. He is not expected to miss much time, according to the report.
Suns coach Alvin Gentry said the procedure was "not a big deal."
"We checked with the doctors, and it's a minor procedure. He [was] just having some gallstones removed," Gentry said, according to the report. "He's supposed to be playing in three to four days and has been cleared to travel next week."
The surgery was first reported by Turkish media, according to The Republic.
Turkoglu, a 6-foot-10 forward, had a disappointing 2009-10 season in Toronto, where he signed as a free agent after helping the Orlando Magic reach the 2009 NBA Finals and winning the NBA's most improved player award.
Turkoglu still needs to pass a physical with the Suns, according to the report.