NBA officials are working with the Mobile Police Dept. to coordinate a surrender date for DeMarcus Cousins in his domestic violence case, cops tell TMZ Sports.

As we previously reported, Cousins is facing a 3rd-degree domestic violence charge in Alabama stemming from a threatening phone call he allegedly made on August 23 to the mother of his child.

Cousins allegedly told his ex-girlfriend he'd put a "bullet in [her] f**king head" if she didn't let their child come to his wedding, which took place in Atlanta the very next day.

An arrest warrant was issued for Cousins days later -- but he had just undergone surgery to repair his torn ACL, which made it difficult for Boogie to travel to turn himself in.

But, Cousins appeared in good spirits at Lakers Media Day last week -- so we called the Mobile PD to see if there's been any movement in that case.

A spokesperson told us officials aren't hunting down Cousins because he's only facing a misdemeanor charge -- but noted "The NBA has reached out to us" to facilitate an official surrender.

We reached out to the NBA multiple times to find out why they're getting involved but, so far, no word back.

But, a source connected to the situation put it this way ... a high-profile NBA player is involved in a high-profile criminal case. The NBA wants to make sure things don't spiral out of control.