Swap space or page file is reserved on the:

The motherboard is a circuit board that connects components; it does not contain addressable storage space for virtual memory.

Physical memory (RAM) is what swap space and the page file are designed to supplement when it becomes full, not where they are stored.

Swap space and the Windows page file are stored on the hard disk (or SSD) as a form of virtual memory. When the operating system runs out of physical RAM, it moves less-active memory pages to this disk-based space to free up RAM for active processes. Because disk storage is non-volatile and much larger than RAM, it serves as an extension of addressable memory space.

The CPU contains registers and cache for immediate computation but has no storage capacity for holding swap or page file data.