Their romance is moving at lightning speed!

Jennifer Lopez and Alex Rodriguez have been inseparable since they began dating last month, and the love birds made no attempt to hide their love as they grabbed dinner at Nobu in Malibu last night.

It sounds like things are already really heating up between the pair!

"Boyfriend and girlfriend titles have been vocalized with each other. What was a hot, casual thing is turning into something more serious. They can't keep their hands off each other in public or amongst close friends. It got really hot and heavy and they want to see where this goes, but are hopeful it can lead into a future," a source dished to E! News.

"All his friends can tell he really likes J.Lo [but] in the beginning they thought this may just be a fling. Friends are slowly thinking this may actually be a great match. He calls J.Lo his lady," the source added.

We have a feeling there's an engagement in J-Rod's near future!