The 69-year-old crooner chatted with reporters and mentioned that he learned about the supposed marriage in the press Wednesday.
On Tuesday, British tabloid The Sun, in a report citing unnamed sources, said that the younger Iglesias and the Russian tennis beauty were planning to marry next week.
Julio Iglesias married Miranda Rijnsburger in 2010 and Enrique Iglesias has been in a relationship with Kournikova since 2002.
Enrique Iglesias turns 38 Wednesday.
Hola! magazine also denied Wednesday that wedding bells were sounding for the singer of Experiencia religiosa.
"There's no Enrique Iglesias wedding," headlined the publication in its online edition.
Not even Enrique's publicist, Joe Bonilla, would confirm that any wedding date had been set, telling EFE: "Enrique is like the tide, always surprising. If he's planning to get married, I'm sure that he's going to surprise us all."