"[JENNIFER Lopez] has always wanted to be on the cover of Vogue," a source close to Lopez told PAGE SIX. "She seems to think that [Benny Medina] was once snubbed by [Vogue writer] Andre Leon Talley, so [Medina] refused all requests for her to be in the magazine."

"Jennifer was styled by all of their top stylists. They brought the clothes, did her hair, everything," says our snitch. "She was supposed to be 'The Millennium Girl' and it was going to be huge. But then nothing happened. Benny called Anna's office and she didn't call him back, because she had decided Jennifer 'wasn't Vogue material.' "

As for the rest, "[Anna Wintour] never said Jennifer wasn't Vogue material, someone else must have said that," [Patrick O'Connell] insists. "And if Jennifer indeed called Anna, then she must not have gotten the message because she would have called her back." He confirmed that further cover talks are taking place.