Gossip website Bossip posted what it alleged to be racy text messages that Swizz Beatz exchanged with a young woman named Christina Elizabeth.
Elizabeth later told the website that she and Swizz Beatz have routinely exchanged texts for the last four years.
She claimed to have had a physical relationship with Swizz Beatz while he was married to ex-wife Mashonda Tifrere, but denied any recent sexual contact.
Elizabeth also said that she recently lost her phone and is not responsible for leaking the messages to the press.
Swizz Beatz has seemingly denied that he is romantically involved with Elizabeth, writing on Twitter: "Wow people sure do take things far with the BS Lmao… If people put the same time into positive things the same as they do negative B.S the world would be a better place! #peopleneedhelp. (sic)"
Keys also addressed the reports of her husband's infidelity by tweeting: "Haaaaaaaaaaa!!!!!!!! Some things are just LAUGHABLE!!!!!! Now, Let's Continue to SHINE!! Everything else is a waste of time!! Sending love."
Keys and Swizz Beatz married on the French island of Corsica in July 2010 and welcomed their first child in October.
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Watch Alicia Keys's 'No One' music video below: