While it is believed that neither of them have actually contacted a divorce lawyer, they are now allegedly 'separated', according to the website.
TMZ claims that people close to the NBA star have been unable to find or contact him for the last 72 hours, although a representative for the star has denied this.
The couple have been subject to persistent rumours that their marriage is in trouble after Lamar allegedly cheated on Khloe with two different women.
But several sources have told TMZ the real reason behind their marriage crisis is that Khloe reportedly believes that her husband has a drug problem.
Earlier this week the Kardashian family allegedly staged an intervention to convince Lamar to return to rehab, but he refused, reports the gossip website.
Khloe urged Lamar in August 2012 to go to rehab and after he entered a San Diego facility she hired private investigators to make sure he didn't leave.
Lamar reportedly constantly threatened to leave the rehab clinic and Khloe visited several times to convince him to stay, but he left after three weeks, sources said.
A spokesperson for the basketball star told TMZ on Sunday afternoon that he was fine but would not reveal his whereabouts.
Lamar, who won two championships with the Los Angeles Lakers, stayed clean and played well last season for the Los Angeles Clippers, but sources said he resumed using drugs after the season.
'Khloe is more concerned about saving Lamar than ending her marriage,' a source told TMZ.
Khloe allegedly tossed Lamar out of the house after the failed intervention, and he was pictured Wednesday as an associated loaded a number of large suitcases into his car in Calabasas, California.
Khloe and Lamar got married in 2009 about a month after meeting each other.
Khloe has recently endured reports that Lamar had an affair with Jennifer Richardson for a year until March 2013 and a six-week fling with lawyer Polina Polonsky at the start of the summer.
I am shocked, was actually one of her fans, praying and believing her marriage would last.....they were so in love, so real....sad!