The 47-year-old announced she had quit the hit show on Tuesday, sparking speculation over who will replace her.
Now Fox Chairman Peter Rice has revealed that the network is searching for an official fourth judge to take over full-time -- but is struggling to find someone suitable.
He says, "There is going to be a search. We love Paula. She's been a really wonderful part of the show for eight years. There is going to be a change and that change we have to look at that as being a positive change. It wasn't a decision we made, but we have to look at it in a positive way.
"We'll have these guest judges do one week each during the audition (period)... there is no thought right now that any of these judges will be long term judge for us. All of the people we are talking to have successful careers. I don't even think they'd be available to judge full-time. We have now until January to introduce a new energy to the panel."
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