Does a USB mouse have memory that could be used to store malware?
Many USB peripherals include flash-based microcontrollers. Although mask-ROM-based microcontrollers are cheaper, use of a flash-based microcontroller may enable a manufacturer to have one board which can go in a variety of OEM products, each of which reports the name under which it is sold. Some peripherals include firmware that allows them to be reprogrammed from the USB port; having them configured that way would allow a manufacturer to pre-program parts in a way suitable for its highest-volume customer and re-program them on demand for other customrs.

If a mouse happens to include a flash microcontroller, it may be possible for a malicious person to reprogram it to behave as a malware-infection device. Because most mice aren't likely to use particularly big microcontrollers, there may not be any room for malware if the mouse is required to be usable as a mouse. On the other hand, it might be possible for some malware to identify a vulnerable mouse and reprogram it in such a way that it would no longer work as a mouse, but would act as an agent of evil when plugged into a non-infected machine [on the theory that someone whose mouse stops working might test it on another computer].

It would in general not be difficult to design a USB peripheral in such a way that once final firmware was loaded it could not be reloaded from the USB port, but there is no general way to distinguish devices which are immune from reprogramming from devices which aren't.  It would also be possible to design a "smart USB hub" with a display and some buttons which would, when a device was plugged in, indicate what the device is claiming to be, asking for confirmation before the computer could see the device, and restricting the device's communications to those that were approved for its type, but I don't know if any such smart-hub devices are available.