Action News has learned through multiple sources that the "inappropriate off-duty relationship" was with the wife of a Fresno Police officer.
Members of the Fresno Police Officers Association met Wednesday afternoon, but the president told Action News it was a regular meeting.
"We didn't feel it would be prudent to take any kind of action while there's an ongoing investigation," Fresno Police Officers Association President Brandon Wiemiller said.
"We've always advocated for due process for our officers, and this would be no different. We haven't called for any kind of action to be taken against the chief," he said.
Action News is also learning the chief could be looking to leave Fresno. The Austin-American Statesman and ABC affiliate KVUE reported Tuesday that Balderrama applied to lead the Austin, Texas, police force. He is one of 32 applicants.
RELATED: Fresno Police Chief Paco Balderrama applies to be Austin's next top cop
"They're really going to be looking for someone with mid-to-big city - actually being a chief of one of those ... of a comparable size department to Austin," Austin American-Statesman Public Safety Reporter Skye Seipp told Action News on Tuesday.
It is unclear when Balderrama put his hat in the race, but the application opened on May 15 and closed on June 10.
Balderrama would have applied well after city leaders became aware of the situation. The city of Fresno says he first approached the mayor and city manager in February to disclose details about the relationship.
The city attorney will not confirm when the investigation into Balderrama formally opened but the city announced it publicly on June 6, four days before the City of Austin closed its application.
"Some of these people you're kind of looking at them - Do you think there's a good chance with your pasts that you could be given this job here?" Seipp said.
It is unclear when the investigation could wrap up or if Balderrama is still under consideration to be police chief in Austin.
Action News has not heard back from Austin officials.
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