The meeting comes as the injury-riddled Oden intensifies his search for a team with the goal of returning to the NBA next season. Ainge confirmed the exploratory meeting.
The Celtics were not previously believed to be a strong candidate for Oden's services, but Saturday's meeting suggests otherwise.
San Antonio, New Orleans, Charlotte, Indiana and Dallas have been monitoring the rehab of Oden and are in the running for his services, sources told ESPN The Magazine's Chris Broussard earlier this week.
Oden is preparing for a return to the NBA next season, with Miami and Cleveland earlier reported as the front-runner to land the 7-footer. Several clubs have been in touch with Oden's representatives about possibly signing him this year, according to league sources.
Oden, the first overall pick by the Portland Trail Blazers in the 2007 draft, is expected to choose a team in the next three to four weeks, according to sources. He would not play, however, until the 2013-2014 season.
Oden is shuttling between Indianapolis and Columbus, Ohio, where he is rehabbing at Ohio State University. Knee injuries have limited Oden to only 82 career games. The 25-year-old underwent the Orthokine procedure championed by Kobe Bryant this past fall.
While most clubs are likely to offer Oden the league's minimum salary, clubs such as Cleveland, New Orleans and Charlotte could offer a much larger payday.
Information from ESPN The Magazine's Chris Broussard was used in this report.