Sauce Gardner is peeling back the curtain on his love life ... telling TMZ Sports things are pretty "cool" with Ice Spice -- and as it turns out, LeBron James had a role in their coupling!!

We caught up with the New York Jets star out in L.A. this week ... and asked him all about his budding romance with the rapper.

While Sauce didn't sing like a bird, he did say he liked how things were going ... and raved about all they have in common -- being based in the Big Apple, experiencing success at a young age and having their fair share of haters.

As for how they linked up ... it turns out the two first crossed paths during a taping for King James' show, "The Shop" -- an episode that aired back in April 2024 and starred Sauce, Ice, Travis Scott, Chad Johnson and the Lakers superstar himself.

Fast forward a year, and the two went Instagram official ... after months of teasing being a pair in the weeks leading up to the hard launch.