Woman Claims Reggie Bush is the Daddy

Reggie Bush is living in a world of uncertainty, because a woman claims he's the father of her unborn baby ... sources tell TMZ Sports.

The woman -- Monique -- is a nightclub waitress who lives in Miami. Our sources say early on in her pregnancy, she contacted Reggie and there were discussions about terminating the pregnancy in return for a large payment. We're told ultimately the discussions went nowhere.

Our sources say Monique, who is now 6 months pregnant, hired Florida attorney Marwan Porter, but this time around it's about child support.

We're told there has NOT been a DNA test, but Reggie will own up to his obligations if the tests show he's the father.

As for Reggie, there appeared to be issues back in August, around the time Monique first contacted him, because he left Buffalo Bills training camp to fly to California to work things out with his wife, Lilit, with whom he has 2 kids.

A rep for Reggie tells TMZ, "He's aware of the rumors and remains happily married."