We do. Or at least, historians who study the Mughal empire do. The general public may not associate the Mughals of India with the Timurids (if they know anything about the Mughals at all), but historians have certainly referred to the Mughal ruling house as the "House of Timur" or "Timurid dynasty," and the Mughal empire as the "Timurid empire." For example, the late John Richards, one of the most eminent historians of Mughal India, consistently uses the term "Timurid" in his book The Mughal Empire (published as part of the New Cambridge History of India series). However, the term "Mughal empire" is generally preferred by historians over "Timurid empire" simply to avoid confusion with the earlier Timurid empire, just as many historians prefer to use "Byzantine" instead of "Roman" simply to avoid ambiguity over what they are referring to.

Regardless of whether modern historians or the general public associate the Mughals with the Timurids, the Mughals themselves certainly associated with Timur, and certainly derived legitimacy from claiming to be his descendants (which of course means they also claimed descent from Genghis Khan and the early Mongol conquerors, hence the term "Mughal" which simply means "Mongol" in Persian). The Mughals' strong sense of attachment to the Timurid legacy can be seen in Shah Jahan's ill-fated attempt to conquer the old Timurid heartland in Central Asia in 1645-47. Abdul Hamid Lahori, a Mughal court historian, describes the motives for this invasion as follows (excerpt from Lahori's Badshahnama, Vol. II, p.482, all emphasis mine):

Ever since the beginning of his [Shah Jahan's] reign, the Emperor's heart had been set upon the conquest of Balkh and Badakhshan, which were hereditary territories of his house, and were the keys to the acquisition of Samarkand, the home and capital of his great ancestor Timur Sahib-Kiran. He was more especially intent on this because Nasir Muhammad Khan had had the presumption to attack Kabul, from whence he had been driven back in disgrace. The prosecution of the Emperor's cherished enterprise had been hitherto prevented by various obstacles, but now the foundations of the authority of Nasir Muhammad were shaken, and his authority in Balkh was precarious. . . So the Emperor determined to send his son Murad Bakhsh with fifty thousand horse, and ten thousand musketeers, rocketmen and gunners, to effect the conquest of that country.