According to a source close to Lopez, the upcoming World of Dance judge and Rodriguez are already considering marriage, Us Weekly reported.
"They've been talking about the future and, of course marriage has come up," the source said of Lopez, 47, and Rodriguez, 41.
Exactly when the couple began dating remains unclear, however the romance is fairly new. Early last month, People reported Lopez and the retired New York Yankee had only been dating "for a few weeks."
"They aren't making wedding plans, but they have been talking about their lives," the source told Us.
The pair's families are reportedly both onboard with the relationship. A Lopez insider said the former American Idol judge's mother, Guadalupe Rodriguez, spent time with the couple in their shared hometown of New York City on April 2.
Meanwhile, Lopez's sister Lynda reportedly thinks the Fox Sports analyst "is very charming and good to Jennifer."
"She hasn't felt this way about anyone in a long time and they are very excited for her," noted the Lopez insider.
As for Rodriguez's clan, his sister Susy Dunand has seemingly welcomed Lopez with open arms. On March 17, Dunand captioned an Instagram photo of Lopez and herself, "#miscunis," which is a Spanish word for in-laws.
"Their families love them together. It's a perfect match," said the source close to the singer and Shades of Blue actress. "They have a lot in common and the same interests. It's going well so far. They are both hoping this goes the distance."
Rodriguez, a 14-time MLB All-Star, has reportedly already been introduced to her nine-year-old twins Max and Emme. In turn, Lopez has met the athlete's daughters Natasha, 12, and Ella, 8, during her recent stay in Miami, FL.
Lopez has never given up on true love. She was previously in a long relationship with her backup dancer Casper Smart, and before him, Lopez wed and divorced Marc Anthony, Cris Judd and Ojani Noa. She had also been engaged to Ben Affleck.
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"I love getting married," Lopez admitted last year, E! News reported. "I really want to get married in a church with a big dress."
Rodriguez had been romantically linked to actresses Cameron Diaz and Kate Hudson in recent years. He split from his now ex-wife Cynthia Scurtis in 2008.
Lopez is set to judge the reality dancing competition with longtime Dancing with the Stars pro Derek Hough -- who has won six mirrorball trophies -- and Ne-Yo, the Grammy Award-winning singer and dancer.