Rodriguez often gifts Lopez presents with handwritten love notes, a source tells PEOPLE


Alex Rodriguez is pulling out all the stops to woo new love Jennifer Lopez.

“Jennifer is still on cloud nine. She has never seemed happier and loves sharing her life with Alex,” says a Lopez source. “He often gives her gifts with handwritten notes. It’s a very romantic relationship.”

Jennifer Lopez Alex Rodriguez

Lopez — who is mom to 9-year-old twins Max and Emme — and Rodriguez — who shares daughters Ella, 9, and Natasha, 12, with his ex-wife Cynthia Scurtis — have gone on tropical vacations together, dined at a slew of upscale restaurants and recently celebrated Easter as one big family with their kids.

“She loves sharing her life with Alex,” adds the source. “The kids all get along and it’s just one, huge happy family.”

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The athlete, 41, is also “very supportive of Jennifer,” who’s back at work on Shades of Blue.

The star, 47, is currently working on her upcoming Spanish album with ex-husband Marc Anthony, “and Alex admires and supports how hard she works,” says the source. “They share this amazing respect for each other.”

And though there are no plans for an engagement yet, “if Alex would propose, no one doubts she would say yes,” says the source.