The quick answer is: no, we do not from our records if he was posed with that question. However, he did have non-Arab companions. So it is very probable the question could have arisen.

Does Islam require adherents to perform their compulsory prayers in Arabic?

No, there is no mandate in the Quran or Hadith on the language of prayer. These two, in that order, are the primary sources of authority in Islam. They are also where the words of Islamic prayers come from. Muslims today pray in Arabic out of convention, and because emulating Sunnah, the conduct of the Prophet Muhammad, is a strong tradition in Islam.

Why is there a focus on Arabic as the primary language of prayer in Islam?

There is a narration (Hadith) where Muhammad says (emphasis mine) his followers should emulate how he prays:

We came to the Prophet (ﷺ) and stayed with him for twenty days and nights. We were all young and of about the same age. The Prophet (ﷺ) was very kind and merciful. When he realized our longing for our families, he asked about our homes and the people there and we told him. Then he asked us to go back to our families and stay with them and teach them (the religion) and to order them to do good things. He also mentioned some other things which I have (remembered or) forgotten. The Prophet (ﷺ) then added, "Pray as you have seen me praying and when it is the time for the prayer one of you should pronounce the Adhan and the oldest of you should lead the prayer. - Bukhari, Vol 1, Book 11, # 604

We can only speculate about why in the early days of Islamic expansion outside Arabia did Arabic remain the dominant language of prayer. In the days of the Rashidun Caliphate, specifically the reign of Usman (644 - 656 CE), the Quran was standardized because of differences in how people were reciting the Quran. Usman commissioned a standardized copy (Bukhari Vol 5, Book 61, #510). This hints that even then, he recognized the importance of consolidating the language of the Quran.

Can adherents pray in their own words?

Yes, Islam does not set a strict requirement for the wording of prayers. For example, another narration is about a person who is unable to learn contents of the Quran. The Prophet instead gives him a shorter prayer to recite:

A man came to the Prophet ﷺ and said: 'I cannot learn anything of the Quran; teach me something that I can say instead of reciting the Quran.' He said: 'Say: SubhanAllah, wal-hamdulilah, wa la illaha ill-Allah, wa Allahu Akbar, wa la hawla wa la quwwata illa Billahil-aliy al-azim (Glory be to Allah, praise be to Allah, there is none worthy of worship except Allah, Allah is Most Great, and there is no power and no strength except with Allah the Exalted and Magnificent ). - Sunan an-Nasa'i, 924

There is very little material from the life of Muhammad about praying in languages other than Arabic. Almost all of the Muslim converts during his lifetime were Arabs. There are very few documented non-Arab companions of Muhammad. However there is little evidence to indicate that they did not know Arabic. A notable companion is Salman the Persian who known for his pursuit of religious knowledge and who partially translated the Quran into Persian.

To conclude, there are no traditions from the time of Muhammad that directly address the question of language of prayer other than Arabic. However, we can see that adhering to the actual Arabic wording of the Quran (and therefore prayers) was considered important by Muhammad and his companions. But adherents were able to pray in their own words as well.