Kardashian, 30, reportedly spent the recent Thanksgiving holiday with model Aubry, 34, and a pal said to PEOPLE: 'He likes how family-oriented she is.'
The reality star also reportedly appreciated how devoted he is to his two-year-old daughter Nahla, whose mum is actress Halle Berry.
Kardashian is said to be 'trying to take it slow' despite the fact he met her entire family over Thanksgiving.
The new couple spent the evening together before Aubry spent the following day with his little girl.
A friend of the pair said: 'She likes that he's so cool and relaxed. He's great.'