The 39-year-old socialite has been dating the 38-year-old comedian since June and although they have been having the ''best sex ever'' she isn't keen on making their relationship serious.
A source told the Daily Star newspaper: ''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.''
However, Russell is in thrall of Jemima and is keen to make their relationship an ''exclusive'' one.
A friend of the actor said: ''Russ surprised us all by how taken he is with Jemima. He's desperate to take things to the next level and make things exclusive.
''It's like he's addicted to her. She's described him as compulsive and obsessive and it's too much.''
Russell has a notorious reputation as a ladies man and was previously married to Katy Perry, Jemima's ex-husband is Pakistani cricketer-turned-politician Imran Khan and she also had a long-term relationship with actor Hugh Grant.
The singer introduced "the next generation" in Iceland.
Jack Antonoff hears a ''female voice'' in his head when he writes music.
The show will be seen by everybody at the same time.
The Scottish comedian has been speaking about gaining a knighthood in the Queen's Birthday Honours List.