Kanye announced they are expecting their first child together at one of his concerts last week. Although many other stars chose to debut their children on the pages of glossy magazines, the reality TV star and her hip-hop guru lover want to be low key.
According to TMZ, they have already been "flooded" with big money offers for the first images of the tot - even though Kim is only just thought to have passed the 12 week mark.
Several publications are thought to be willing to stump up over $1 million, with a non-American tabloid proposing a fee of $3 million.
Despite the large sums on offer, the couple has apparently decided not to sell pictures of their baby at the moment. It's thought they are yet to choose if they will go down that route once the child is born in early summer.
A number of celebrities have sold images of their newborn children, usually to avoid scrums of paparazzi fighting to get the first pictures. Brad Pitt and Angelina Jolie were famously paid $14 million for photographs of their now four-year-old twins Knox and Vivienne, donating the money to charity.
Beyoncé Knowles and Jay-Z decided against following that path when they became parents to their daughter Blue Ivy last year. Instead they released her first pictures themselves on a special website they set up.
Kim is also thought to have decided her baby won't appear on her reality show Keeping Up with the Kardashians.
The 32-year-old star was spotted enjoying a meal out with friends in Miami last night. Despite being with child, Kim stuck to the figure-hugging dresses she usually favours. She opted for a tight blue frock, which boasted cut-outs over her chest and showed the faintest hint of a baby bump.