The reptile, which resembles an alligator, was estimated to be 3 feet long and was discovered by a diver searching for golf balls in a pond near the second hole of the nine-hole course on Stevenson Place.
Ken Powell, the general manager of the golf course, also spotted the caiman today, saying he "saw it roll over" in the water.
But two trips by Tri-City Animal Services personnel to the course have not resulted in a capture.
"Some of the employees are keeping an eye out," Tri-City Animal Services Sgt. John Dauzat said. "It's important for us to spot the exact location where they're nesting to try to get it out."
Dauzat said the caiman could have come from a homeowner near the course, although it is illegal to own such a creature.
"More than likely it was someone's pet, but it got too big for them to handle and they released it in the area," Dauzat said.
A caiman was also found in Fremont last August in a ditch near Irvington High School, but Dauzat said the two cases probably aren't related.
"A lot of people have pet alligators or pet caimans even though they're not supposed to own them," Dauzat said. "Pet stores don't sell them, so they have to go pick them up across the border."
If found and captured, the animal spotted in the pond will be given to a local reptile rescue group.