Schiffer recalled the incident on The Jonathan Ross Show in an episode set to air Saturday on ITV in the U.K.
"I declined, and some other supermodel took it... It's not all about money. I just want to be able to walk down the street and be proud of what I do."
She does not reveal the prince's name, nor the supermodel who accepted the offer.
Schiffer, 43, married film director Matthew Vaughn in 2002. The couple have three children together, Caspar, Clementine and Cosima. The relationship was marred by rumors in 2011 that Vaughn had fathered Mad Men actress January Jones' son Xander. Jones has repeatedly refused to name the father of her son, and Vaughn and Schiffer remain together.