"Everything is on hold right now while she's with Lamar," the insider told Us of Kardashian, who hasn't left Odom's side since he was hospitalized early last week and spent four days in a coma from a drug overdose he suffered while partying at a Nevada brothel.
Kardashian and Harden, an NBA player, took their romance public in July when they were spotted together in Las Vegas. The next month, Kardashian reportedly threw Harden a massive 26th birthday party with many celebrities, including Kim Kardashian's husband Kanye West and fellow NBA players, in attendance.
In recent months, Odom was allegedly upset about his estranged wife dating Harden. Odom, 35, ambushed Kardashian when she was on her way into a SoulCycle class in August to talk about things -- an incident Odom later denied -- but she quickly left the scene to hang out with Harden instead.
"Lamar has been hating that Khloe is with James," a source told Us at the time. "Lamar wants her back. That's what stopped the communication on her end."
Odom was reportedly transferred from Sunrise Hospital in Nevada to Cedars-Sinai Medical Center via helicopter on Monday after he made progress speaking in short phrases, breathing on his own and moving his arms and legs since waking up Friday morning.
Kardashian and her family want Odom, a former NBA star, in Los Angeles so they can be closer to him as he recovers.
Kardashian is still legally Odom's wife although they filed divorce paperwork in July. She was "inconsolable" last week when Odom's condition appeared very grim, according to the source, adding that the reality TV star "hasn't showered" and is "exhausted."
"Khloe is committed to staying with [Lamar]," another source previously told the magazine. "It's a slow process, but Khloe is there every step of the way...It's all been so draining and emotional. It's all baby steps, very slow... He's talking more. He's very slowly improving. It's going to be a struggle."