Lopez has 9-year-old twins from a marriage to singer Marc Anthony that ended in 2014.
The source adds: "He was with her in Vegas during this latest leg of her Planet Hollywood Vegas show".
I'm not saying I couldn't see these two coupling up, but I could just as easily see the rumors as a clever publicity maneuver as Lopez celebrates Season 2 of her show Shades of Blue and prepares for her new reality show World of Dance. "It is definitely for real".
Prior to hooking up with Rodriguez, Lopez reportedly enjoyed a brief fling with Drake. On the other hand, Rodriguez was with Silicon Valley CEO Anne Wojcicki for less than a year.
Both stars recently broke off high-profile relationships.
Rodriguez, who retired from Major League Baseball last August, recently accepted a job as a full-time MLB analyst with Fox Sports following trial runs as part of the network's postseason studio coverage in 2015 and 2016. An Instagram post he shared Wednesday about his Fox Sports gig was liked by Lopez.
Rodriguez, 41, has also spent time around the Yankees during spring training in his new role as a special advisor to the Bronx Bombers. "He wants research. He's nearly all-in to the point where it's annoying".