The 9-month-old daughter of footballer David and fashion designer Victoria was directly addressed in the offer from My1stYears, OK reports.
"Both your parents are fashion icons, and we can see no reason why you shouldn't start your own career in the fashion industry even at your young age," the note reportedly read.
"Due to child labour laws we cannot negotiate a contract or salary directly with you, that is why your Mummy and Daddy have been copied in on this letter."
It continued: "We are happy to speak with them about your fee; however, we are prepared to pay you a significant amount to be the face of our new range."
In February, Victoria Beckham unveiled a range of handbags named after her daughter.
The former Spice Girl has also acted as guest creative designer for a new limited edition Range Rover Evoque.
> Chantelle Houghton: 'My daughter will beat Harper Seven's fashion'
Watch a clip of Victoria Beckham's New York Fall 2011 Fashion Week show below: