The 47-year-old singer appeared to share a first photo with the 41-year-old former MLB star on Instagram following her reported split from Drake.
Lopez posted a grainy picture Sunday on Instagram Stories of a man, who looked like Rodriguez, kissing her head. She quickly deleted the photo.
Lopez and Rodriguez arrived in the Bahamas on Friday and are staying at Bakers Bay Gold & Ocean Club, according to Page Six. The pair first sparked dating rumors last week after reportedly meeting through mutual friends.
"[They were introduced by] mutual friends who put this idea together," a source told Entertainment Tonight.
"Alex and Jennifer ran into each other about a month or so ago in L.A.," the insider added. "They're both single, have these huge careers and their families are their No. 1 priorities. They have a lot in common and friends thought they could be really good together."
Lopez shares 9-year-old twins Max and Emme with ex-husband Marc Anthony, while the former New York Yankees star is dad to two daughters, 12-year-old Natasha and 8-year-old Ella, with ex-wife Cynthia Scurtis. Lopez split from Drake in February.
"This is very, very new," a source recently told E! News. "Jennifer and Alex are both not looking for a relationship, just a good, light-hearted time. They are on the exact same page."