Desert Panther

The Desert Pumas were rare sand-colored cats of Haradwaith, known to attack any man entering its hunting area, for these  were extremely territorial.

Speculations
Since the term Puma usually refers to the american Cougar or Mountain Lion, it seems likely that the desert pumas of Middle-Earth may rather correspond to a distinct race of the Puma genus, such as the Puma pardoides, a cat native to prehistoric Eurasia.