The 43-year-old retired baseball star is very happy in a relationship with the 49-year-old singer now, but he admitted she was a ''big time global superstar'' while he was just a ''young ball player'' when they first met two decades ago.
He took to Instagram to share a black and white photo of the 'On the Floor' hitmaker which was signed ''To Alex, with love, Jennifer Lopez''.
He captioned the image: ''#TBT to almost 20 years ago when a big time global pop superstar signed a pic for a young ball player,'' A-Rod captioned the shot adding, ''#lifecanbeafunnythingsometimes #pictureperfect #keepsake #jlo.(sic)''
And the 'Dinero' singer was shocked by the post.
She commented: ''Omg!! Who found that!!???''
Jennifer later reposted the photo on her own Instagram account and explained how it had resurfaced.
She wrote: ''Wow!! Had to repost!!! He found this cleaning out storage!! (sic)''
Alex - who has Natasha, 13, and Ella, 10, with his former wife Cynthia Scurtis - recently admitted he thinks his relationship with the 'World of Dance' judge works so well because they've shared similar experiences throughout their lives.
He said: ''We're in our forties. We're both from New York. We both come from Latino backgrounds. We both have two kids. I think we've both been through a lot and can really appreciate each other - both the good and the challenges.''
His comments echo similar ones made by Jennifer - who has 10-year-old twins Max and Emme with her former husband Marc Anthony - when she said timing was everything for them.
She said: ''We were both at a good place in our lives. And I think, maybe if we had met in our twenties, it wouldn't ... you know, maybe not so much. We're too crazy. But now, at this point in our lives, where we both have kids and we both accomplished certain things in our careers and we're kind of in that second act of our lives, we really complement each other.''
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