The music mogul, who worked alongside Abdul on American Idol, revealed that the former R&B star has "got a really good shot".
In an interview with Deadline, he said: "I've always wanted Paula - always been very vocal about that. I missed her the second she left the show. Always loved working with her even though she can be a pain.
"And I've been consistent about this. I don't know what it is about her, but I've always clicked with her. You just have to get that chemistry, and she's right. I've never found anyone better than her."
He added: "I think there's a good chance it will be her. We've agreed that we would meet as many people as possible, and now we're reaching the deadline we've got to make the decision soon. But I think she's got a really good shot."
So far, only Cowell and L.A. Reid have been confirmed for the panel, although Cowell recently hinted that Cheryl Cole is also in the running.