American magazine People cites sources who claim the basketball star voluntarily checked himself into a drug and rehabilitation centre.
Reveal has contacted Lamar's rep for comment.
People's report comes a few days after Lamar was arrested on suspicion of driving while under the influence in San Fernando Valley, California.
The 33-year-old was stopped by police on 30 August and taken to a nearby police station. It was later alleged he'd had his driving license suspended for a year because he refused to submit to chemical testing.
Lamar's rep has yet to comment on the arrest.
The athlete - who starred alongside his wife in E! reality show Khloe & Lamar - has also been plagued by reports of a drug problem and issues in his marriage. Khloe's rep had no comment when contacted by Reveal, while Lamar's did not respond.
Khloe, normally a prolific tweeter, has not posted on her social media account since 2 September, when she shared an image from Katy Perry's Labor Day party, which she attended without Lamar.
Prior to that she posted a cryptic tweet reading: "As much as I wish I were made of steel... I'm not… I'm pretty damn close to it though hehe."