"I think that somebody owns it or has it illegally, you know, because it's dangerous to have an animal like that in a neighborhood," James De La Mora told KHOU.
Police were called to the scene but were unable to find any evidence of an animal.
On Tuesday, police were again called for a possible monkey sighting in the area. A 90-minute search yielded no primate.
There were also posts on social media indicating a primate attacked pets and people, however, there were no images or videos included. Authorities and wildlife officials contacted the people who made the posts but did not get replies.
“The Santa Fe Police Department has been unable to substantiate that there is a primate on the loose, or that anyone has been attacked,” officials said in a statement.
But authorities said they are not ruling out the possibility.
"I'm not saying that there is no monkey. In fact, I'm sure there is one on the loose. Out here, anything is possible," Santa Fe Police Department spokesman Lt. Greg Boody told KTRK.
It's unknown if the animal is owned by anyone in the area. Owners of primates and other exotic pets are required to have a wildlife diversity permit issued by the state. All licensed primates were accounted for, KTRK reported.
Primate experts were called in to help. A drone was also deployed during the search, but it did not reveal anything. The search was suspended and the animal is believed to be in hiding.
"We covered a lot of ground but if it's scared and hiding, we're not finding it," Sarah Haywood, the director of Bayou Animal Services, told the Galveston Daily News.
Because the reports of sightings may be rumor, officials are not quite sure what type of primate is potentially on the loose.
Texas wildlife officials said they believe it could be a chimpanzee, KHOU reported. Animal shelter officials said they think it could be a capuchin monkey.
"We'd take it seriously, no matter what," Haywood told the Galveston Daily News. "We're hoping it's not a hoax, because that would be a severe waste of time."