Lopez, 49, played it coy on "The Ellen DeGeneres Show" Thursday when DeGeneres teased her about possibly tying the knot with the former baseball superstar.
“He said that y’all are going to be getting married,'' DeGeneres said.
“He did not say that,” Lopez replied. “He did not say that.”
DeGeneres claimed that A-Rod, 43, had texted her earlier to tell her the news. Lopez asked to see her phone.
"I don’t have my phone with me. I’m working,'' DeGeneres joked. "So you’ll be getting married?”
"I don’t know,” Lopez said. “I don’t know."
Lopez has been married three times, to Ojani Noa, dancer Cris Judd, and most recently singer Marc Anthony, with whom she shares 10-year-old twins Max and Emme. Rodriguez has daughters Ella, 10, and Natasha, 14, with ex-wife Cynthia Scurtis from his first marriage.
Rodriguez and Lopez have certainly been having a lot of fun with each other, whether it's A-Rod and some friends tricking Lopez with a "magic" prank, embarrassing their kids together, or having the time of their lives singing along to "Dirty Dancing" songs in the car.
“You should (get married) because y’all seem very happy,” DeGeneres said to her.
"We are,'' Lopez said. "We’ve been together a couple years. It’s nice."
DeGeneres suggested that Christmas would be a great time to get married.
“I feel like I just made it through Thanksgiving,” Lopez said. “December 1, I start thinking about Christmas. It’s not December 1 yet, right? … I haven’t thought about (Christmas).”
“You’re not leaving here until we find out,” DeGeneres joked.