Wow - what a surprise! Tennis star Anna Kournikova and Spanish singer Enrique Iglesias welcomed twins Saturday at a Miami hospital, according to a report by TMZ.

A source tells the site the babies' names are Nicolas and Lucy -- so, a boy and a girl -- and that Anna specifically tried to stay out of the spotlight the past nine months during her pregnancy. That's not unusual for the highly-private couple who tend to stay out of the press. They've been together since 2001 and it's been speculated for years that the two secretly married, though they've never confirmed.

The former professional athlete did post this Instagram pic on Saturday -- the day she supposedly gave birth -- but it could be an old photo ... or fake news!

Kournikova posted this video in August, which in retrospect, seems to be proof of a baby bump ...