The celebrity couple Enrique Iglesias and Anna Kournikova This celebrity couple first dated in 2001. Enrique Iglesias and Anna Kournikova met during the shoot of the music video, "Escape." There is no confirmation as to whether the celebrity couple already tied the knot. In 2011, Anna Kournikova discussed in an interview the subject of marriage. Vaguely, she said, "I'm in a happy relationship - that's all that matters." On the other hand, Enrique Iglesias shared to E! News in 2016 his thoughts about marriage. The musician said he did not "believe you need a piece of paper to show you love someone." However, in Anna's Instagram account, she has added "Iglesias" after her name.