The three-time American League MVP and 14-time All-Star was sitting in a waiting room for a workout class on Wednesday when he had the conversation with the woman.
Rodriguez, 43, retired after the 2016 season. He made more than $400 million in salary during his decorated Major League Baseball tenure.
The woman pulled out her phone, claiming that the man sharing the room with her looked like the former MLB star. Rodriguez gave a wink to the camera before playing along.
"You've got me thinking now," Rodriguez said.
"Yeah, A-Rod. Alex Rodriguez. There we go," she said.
"Who's that?" Rodriguez asked.
"That's the guy that JLo is dating," she said.
"You're kidding me," Rodriguez replied.
Rodriguez asked if the man looks like himself and the woman said "kind of," before Rodriguez asked for proof.
"Let me see," he said.
The woman then put the phone up to his face and said "it does look" like Rodriguez. She also said it wasn't a good picture of him.
"First of all, I would never wear pajamas that goofy," Rodriguez said. "I mean, what a tool."
She then pulled up another picture. Rodriguez said the man looked nothing like him.
"Are you? You're not, right?" the woman asked.
Rodriguez then stood up and shook her hand saying it was nice to meet her.