"Any allegations against this show we take quite seriously," Fox Entertainment President Peter Liguori said Thursday, calling the competition's credibility "extraordinarily important to us."
Liguori refused to say if Fox and producers Fremantle Media and 19 Television would fire Abdul if the claims by Corey Clark, an unsuccessful contestant on season two, were found to be true.
The probe's results are due soon and will be made public, Liguori said in an appearance before the Television Critics Association.
Abdul, Clark and "corroborating witnesses" have been questioned, he said.
The series, the most-watched on television and a key part of Fox's ratings success, was hit by a tabloid story and then an ABC report detailing Clark's allegations against Abdul. He claimed she advised him on his singing and appearance during their alleged relationship.
In an apparent display of network support, Abdul has been included in another Fox talent contest airing this summer, "So You Think You Can Dance." And while Liguori was before the critics' group, she was filling in as an anchor on a local Fox news show.
A call to her publicist seeking comment was not immediately returned Thursday. In the past, Abdul has denied the allegations.
Although auditions for the fifth season are looming in August, Liguori said the investigation would not be rushed despite uncertainty over Abdul's continued participation in the show.
He noted that not all the judges have been on hand for previous auditions. "That could be a potential option," he said, suggesting that Abdul might be left out in the early going.
Production pressures will not affect the investigation, he said.
"I'd rather be able to come to a conclusion with the independent counsel and our production partners and come out with a definitive answer and conclusion for you," he told the critics' group, "rather than race to have a conclusion before production starts."