Indirectly, it has been deduced that the origin of KREEP is contained in the origin of the Moon. This is now commonly thought to be the result of a rocky object the size of Mars that struck the Earth about 4.5 billion (4.5×10) years ago. This collision threw a large amount of broken rock  into orbit around the Earth. This ultimately gathered together to form the Moon.
Given the high energy such a collision would involve, it has been deduced that a large portion of the Moon would have been liquified, and this 
formed a lunar magma ocean. As the crystallization of this liquid rock proceeded, minerals such as olivine and pyroxene precipitated and sank to the bottom to form the lunar mantle.
After the solidification was about 75% complete, the material anorthositic plagioclase began to crystallize, and because of its low density, it floated, forming a solid crust. Hence, elements that are usually incompatible (i.e., those that usually partition in the liquid phase) would have been progressively concentrated into the magma. Thus a KREEP-rich magma was formed that was sandwiched at first between the crust and mantle. The evidence for these processes comes from the highly anorthositic composition of the crust of the lunar highlands, as well as the presence of the rocks rich in KREEP.