The 42-year-old baseball shortstop has admitted his two daughters Natasha, 12, and Ella, nine - both of whom he has with his ex-wife Cynthia Scurtis - are fans of his new beau Jennifer, as she's a ''great role model'' for them.
He told 'Entertainment Tonight': ''My girls adore Jennifer. She's a great role model and they want to do exactly what Jennifer does. They want to sing, they want to dance, they want to produce, they want to direct. A lot of people don't know she's also a great athlete and great business person, and for me, I'm the luckiest father in the world to be able to expose my beautiful daughters to someone as brilliant as Jennifer.''
And it isn't just Alex's daughters who have given their relationship the seal of approval, as friends of the 48-year-old 'Shades of Blue' actress - who has nine-year-old twins Emme and Max with her ex-husband Marc Anthony - are convinced there is ''marriage potential'' between the pair.
A source said recently: ''Those in J.Lo's inner circle see her relationship with A-Rod going the distance. They definitely see marriage potential here. J.Lo loves that they have so much in common. They're both parents and they're both successful in business. Their lives, while busy, really complement each other.''
Meanwhile, Jennifer and Alex are ''incredibly happy''.
An insider shared: ''They are incredibly happy. Jennifer is on another level for Alex when compared to his past girlfriends. She's amazing. She comes to this dinner and there are 20 people there, a lot of sports celebs and big guys in the business, and she can sit right down with them and start talking sports. She loves baseball.''
'Smalls Change (Meditations Upon Ageing)' arrives in April.
The two awards have made for a great 72nd birthday present for the country music icon.