AceShowbiz -

Are Jennifer Lopez and Alex Rodriguez going to have a baby together? Rumor has it, the "Ain't Your Mama" singer is "so in love" with Alex that she wants to conceive a baby with the former professional baseball player.

"J.Lo's so in love with A-Rod that she's committed to having a baby with him!" a source close to the "Booty" hitmaker reveals to Radar Online, "She knows there's a risk, but she's willing to take it with him!"

The source continues, "Alex is one of the few guys in the world that can make Jenny feel starstruck. She's a huge Yankees fan! She's from the Bronx, after all - and she considers him a legend!"

J.Lo reportedly introduced Alex to her 9-year-old twins, Max and Emme, "shortly after they started dating." He even got a thumbs-up from their father, Marc Anthony, too. "Marc is thrilled to see Jen with a true family man," another source says, "He was always worried about the younger guys she dated, like Drake and Casper Smart."

"Jenny knows Alex hasn't been a great husband or faithful boyfriend in the past," adds the second source, "She's given him a few months to prove he's committed to her, and even put a private eye on him to make sure he passed the test. He has ... so far."