Although published reports said the couple tied the knot in a secret ceremony in Puerto Vallarta, Mexico, a few weeks ago, a source insists to PEOPLE that it's not true: "They definitely did not get married. They're very happy together, but marriage is not something that they're planning in their lives right now."
Kournikova, 23, has a policy of not speaking publicly about her personal life, and Iglesias, 29, has declined comment.
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What's more, this source says Kournikova and Iglesias have not been in Puerto Vallarta together since mid-October, weeks before their alleged wedding supposedly took place.
The couple began dating in 2002, shortly after Kournikova made an appearance in Iglesias's music video "Escape."