Khan, 39, is said to be dating the 38-year-old comedian since June but she is not keen on making their relationship serious, reported Contactmusic.
"They do get along great and have a lot in common, but she doesn't think he's mature enough for her to consider a serious relationship. And until he proves otherwise, she has said she can only see him on a casual basis," a source said.
However, Brand is in awe of Khan and keen to make their relationship an exclusive one.
Brand was previously married to pop star Katy Perry whereas, Khan is the mother of two with former husband, Pakistani cricketer-politician Imran Khan.
