Kim Kardashian, Khloe Kardashian, Kourtney Kardashian, Rob Kardashian and their mother Kris Jenner have all reportedly signed on for the series, which will air towards the end of the year.
> Kanye West: I didn't call Kim Kardashian my Beyoncé'
A source told The Mirror: "The family really feel that they've conquered reality TV in America with a number of different shows and spin offs, so the UK is the next country they want to break.
"The Kardashians love England and think they could get up to a lot of fun - and trouble - with a summer in London. It would make great TV as well as boosting their profile internationally."
The family are reportedly negotiating with West End nightclubs and arranging permits to record in the city.
It was reported last week that Kim Kardashian intends to run for Mayor of Glendale, California.
A spokesperson for the socialite confirmed that she wants to "help and support the Armenian community" in the area.
Rumours that Khloe Kardashian was pregnant were dismissed recently by a US source.
Watch the Kardashian sisters lip-sync to 'Lady Marmalade' below: