That's quite strange question to ask Mongolians, since those people were more "Turkic" than "Mongol". The only thing "Mongol" about them is being Chingizids (Genghis's descendants).
For example, the Golden Horde or Jochi's Ulus (Jochi was the eldest son of Genghis) was already turning Muslim generation after generation and the state language there was Turkic, not Mongol. The state religion became Islam with the rule of "Uzbek" khan (changed name to "Uzbek" after adopting Islam). Since then muslim people of the Golden Horde were unofficially called Uzbeks (and that's how the modern day Uzbeks got their name).
Same with Taimur (Tamerlan), who was Turkic by ethnicity and spoke Karluk language (practically Turkic language nowadays).
Interesting fact: Uzbeks of that time and Uzbeks nowadays are almost completely different people. Uzbeks of that time (Nomadic Uzbeks to be more precise) were Nomadic Tribes living in modern day Kazakhstan. In mid 15th century, when some Nomadic Uzbeks were discontent with the rule of new Khan (Abulkhair), they declared "independence" from Abulkhair Khan. So these "vagabonds" were named "Uzbek Kazakh", which meant "independent from the khan of Nomadic Uzbeks. Later the Uzbek part fell off and that's how Kazakhs became known by that name. So Uzbeks of that time are actually modern-day Kazakhs.