Is it possible to reprogram wireless mouse receiver to receive signals from different mouse

Tricky, since the Logitech seems to be using a proprietary radio protocol, I think. If it was Bluetooth I would not expect this type of interference since that uses the whole of the 2.4 GHz band, changing frequency 1600 times a second so it is only ever on one particular frequency for a very tiny fraction of the time.

My guess is that the Logitech is using one or one of a very small number of narrow-band frequencies, and this happens to fall within range of your wi-fi signal. A more reliable way to beat the interference would be to change your wi-fi access point (or router with built-in AP) to a different channel, as far away from the current one as possible (eg go from 1 to 11, or vice versa).

Unfortunately the Microsoft peripherals do not seem to support this usage. You might want to look in to upgrading to Logitech Unifying devices, which use a universal micro receiver. Logitech tends to be on the pricey end, but I'm not aware of anything at a lower price point with proper universal receiver functionality. You could just look in to buying a Microsoft keyboard and mouse as a set, since they'd come together with one receiver for both.