Kardashian, 30, filed for divorce from the 34-year-old basketball player last December but he still hopes to get her back and apologises for everything he put her through before they split, reported Ok! magazine.
"He sends her favourite flowers all the time just to make her smile. Kris (Kardashian's mother) has always held a special place in her heart for Lamar, so when he reached out to apologise to her too, she was like putty in his hands.
"Lamar knows that even if he earns Khloe's trust back, it's her mom who makes all the family decisions. He's thrilled they're talking again," a source said.
Odom, however, has reportedly changed a lot in recent months. "Lamar is clean and sober now. He's been seeing a therapist and working out regularly, getting himself on the right track to win Khloe back," the source added.
Kardashian recently ended her relationship with rapper French Montana, whom she started dating in April.