The couple welcomed little Saint into the world on December 5 and since his birth, they have been inundated with offers from publications keen to show him off for the first time.
According to tmz.com, offers range from $2 million to $2.5 million and request the full family, including Saint's older sister North, two, to take part in a range of pictures, including candid group shots.
However, insiders told the website the couple are "almost certain" they will reject all offers for the pictures.
When North was born, Kanye, 38, showed off a selection of pictures of her on his mother-in-law Kris Jenner's now-defunct talk show, fuelling speculation that Saint's public debut will come on Kim's sister Khloe Kardashian's new programme "Kocktails with Khloe", which launches in the new year.
The family have already been seen in public together since Saint's birth, but during the visit to take the infant to the doctor last week, Kim, 35, and her rapper husband ensured he was kept fully covered and away from view in his car seat.
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