The meeting was to take place in Los Angeles, sources said.
The Houston Rockets also have secured a meeting with Iguodala, league sources said.
Teams began talking to free agents at 12:01 a.m. ET Saturday, but no deals can be officially signed until Thursday.
The Spurs feel as if they have a legitimate shot at luring the Golden State Warriors' prized sixth man away from the San Francisco Bay Area, sources said. Iguodala is open to relocating under the right parameters, according to sources.
Iguodala doesn't yet have plans to meet with the Warriors, sources said earlier.
The Warriors are expected to target free-agent forward Rudy Gay if Iguodala lands elsewhere, sources told ESPN's Adrian Wojnarowski.
Iguodala also will meet with the Sacramento Kings, sources said. The Kings are trying to acquire solid veterans to play with their stable of young talent.
The 33-year-old Iguodala, the 2015 NBA Finals MVP, has been a terrific two-way player since being acquired by the Warriors via trade in 2013.
Despite just one start over the past three regular seasons, he has posted averages of 7.4 points, 3.7 rebounds and 1.1 steals in 26.6 minutes per game. The 6-foot-6 swingman was a finalist in 2016-17 for NBA Sixth Man of the Year, finishing second behind Eric Gordon of the Rockets.
Iguodala holds career averages of 13.0 points, 5.3 rebounds, 4.5 assists and 1.6 steals per game since breaking into the league as the ninth overall pick of the Philadelphia 76ers in the 2004 draft.
Information from ESPN's Ramona Shelburne was used in this report.