Supervisor Hank Kuiper said the issue was broached more than once at a social event he attended Friday and he was asked if he was "the third vote" to fire Capela.
Kuiper said he is happy with the job Capela is doing. He said he does not know the source of the rumor.
"I would have to think it's from within the organization," he said. "We just wanted to make sure the rumor is stopped."
Capela said the issue came as a surprise.
"I had no idea any of this was happening," she said after the meeting, adding she was pleased with the supervisors' comments. She said she was just in the process of scheduling meetings with the supervisors to discuss her performance, as the board membership is different than when she became CEO back in November. "I have not seen any friction between me and staff or even elected officials."
Supervisors Chairman Tony Tirado said he became aware of rumors circulating about the issue about two weeks ago.
He said the rumor came from among county staff members or department heads.
"That's the way I see it," Tirado said, adding in the shift from county administrative officer to CEO system there would be some pain. "There's no question that to some point there is friction."
The CEO position wields more authority than did the former position.
Tirado said despite not seeming as enthusiastic as other board members in his public comments about Capela at the board meeting, he fully supports her.
He credited himself with the idea of a CEO and said he wants to ensure the position is successful but that the success be in the best interests of the Imperial Valley.
Supervisor Wally Leimgruber said individuals have expressed their concerns to him and that the concerns have been discussed with Capela.
Leimgruber's public comments also were not as supportive of Capela as were Kuiper's and Maruca's, but he said he "indeed" supports her.
Separately, the board denied there is movement afoot to increase supervisors' pay by 45 percent.
Supervisor Gary Wyatt is recuperating from heart bypass surgery and was not at Tuesday's meeting.
Staff Writer Rudy Yniguez can be reached at 337-3440.