A source previously told WHO Rodriguez, 41, is pulling out all the stops to woo his new love.
“Jennifer is still on cloud nine. She has never seemed happier and loves sharing her life with Alex,” a Lopez source said. “He often gives her gifts with handwritten notes. It’s a very romantic relationship.”
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,” the source added. “The kids all get along and it’s just one, huge happy family.”
Rodriquez is also “very supportive of Jennifer” — FaceTiming her on the Shades of Blue set this week before stopping by on Friday and sharing a live video to Instagram for his fans.
So are wedding bells in the air? Perhaps! Though there are no plans for an engagement yet, “if Alex would propose, no one doubts she would say yes,” a Lopez insider previously told PEOPLE.
This article originally appeared on PEOPLE