"Khloe has been very, very hurt by everything. There is a lot about Lamar that she is just learning and if they have any chance of making this work, there is a lot they need to come to terms with," the source explained.
"They both really want to make this work. But they are not sure if they can. This is the first step to see if they have a chance of healing and moving on. Only time will tell."
According to People, Kardashian, 29, and Odom, 33, are getting therapy separately in addition to their joint sessions, and the reality TV star's family is "supporting [Lamar's] recovery."
The two have reportedly been spending increasingly more time together following a very rough summer.
Kardashian and Odom, who have been married for four years, attended Kris Jenner's birthday celebration earlier this month and were "getting along very well and were couple-y together," said another E! News source.
"It was very intimate and everyone was really pleased to spend time with them."
Kardashian and Odom also went to Kanye West's concert at the Staples Center in Los Angeles last month, which marked their first public outing together in months. However, TMZ claimed at the time their hangout session wasn't indicative they're reconciling or getting back together.
In addition, the NBA basketball free agent is allegedly pals with Kardashian's stepfather Bruce Jenner and they're very close.
"They relate to one another," the second source told E! News. "They are both athletes and Bruce has always been a great advisor to Lamar. Lamar deeply respects him."
Odom insisted late last month his relationship with Kardashian has been "wonderful" and they're "unbreakable."
"That's why I wear my wedding ring. It is a beautiful ring," Odom told Us Weekly in October. "From a beautiful wife."