Christy West, according to TMZ, alleges that Cousins said he would put a "bullet in (her) f---ing head" during an argument over allowing their 7-year-old son to attend Cousins' wedding to another woman.
The NBA said in a statement on Tuesday that they are aware of the reporting and are "investigating the allegations."
The Lakers said they are also looking into the matter.
"We are aware of the allegation involving DeMarcus Cousins and, of course, take this claim seriously," the Lakers said in a statement. "We are in the process of gathering information and will reserve further comment at this time."
Cousins declined to comment when reached by ESPN.
TMZ shared an audio recording West took of the incident and she says that the male voice heard is that of Cousins.
During the argument, the man says, "I'm gonna ask you this one more time before I take it to another level ... Can I have my son here, please?"
After West responds "No," the man makes the threat and the audio clip ends.
Cousins got married in Atlanta this past Saturday, and his son was not there, according to TMZ.
The 29-year-old former All-Star suffered a torn ACL earlier this month and could miss the entire season -- his first with the Lakers.
A lot still to know about Cousins allegations
Reporter Jason Jones expresses surprise regarding the allegations of DeMarcus Cousins threatening his ex-girlfriend during an argument.