The couple's relationship has been on the rocks for months amid allegations the basketball star, 33, recently battled an addiction to crack cocaine and cheated on Khloe with several different women, reported E! online.
The duo is yet to make a decision about the future of their marriage.
"They have been spending an increasing amount of time together. At one time it seemed like a reconciliation was impossible and divorce was inevitable. Things may have turned a corner," a source said.
Former Los Angeles Lakers player, Odom, was recently spotted with Khloe, 29, at her future brother-in-law Kanye West's concert in LA, marking the first time they have been spotted in public together in weeks.
The brunette beauty also changed her name on her Instagram and Twitter profiles by removing her last name Odom.