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Meanwhile, rumors have been swirling that Rodriguez has been seen making late night visits to married Madonna's Manhattan apartment -- a claim the pop star's spokeswoman has denied.

The Post cited unnamed sources who said Rodriguez's wife, Cynthia, has been in Paris with Kravitz for the past several days, while Cynthia's two young daughters with A-Rod remained in Miami.

Insiders told the Post no divorce papers have been filed, however, they said both Alex and Cynthia now consider their marriage over.

Kravitz, who collaborated with Madonna on her 1990 single, "Justify My Love", denied speculation he had an affair with the U.S. pop star at the time, the Post said.

Kravitz also denied an affair with Cynthia Rodriguez, issuing a statement to Usmagazine.com that said: "There is absolutely no affair between Cynthia Rodriguez and myself. This is unequivocally 100 percent not true. Cynthia is a friend and is here with the godfather of her baby, who is also Alex's trainer, his wife and their baby girl. She came here to escape from everything happening in New York City. I opened my home to her as a friend and I find it extremely hurtful that I am now being referred to as an adulterer."

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