Assalaamu alaykum. Is there any hadith that indicates that Europeans will convert to Islam near the End of Time?

All perfect praise be to Allah, The Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallahu ‘alayhi wa sallam, is His slave and Messenger. 

As far as we know, there is no hadeeth that clearly states that. However, some scholars deduced this meaning from the following hadeeth, which was narrated on the authority of Al-Mustawrid Al-Qurashi, may Allah be pleased with him, who said, “I heard the Messenger of Allah, sallallahu ‘alayhi wa sallam, say, 'The Hour shall come with the Romans forming the majority of the people.'” [Muslim]

Ibn Katheer wrote, “This indicates that the Romans will embrace Islam at the end of time, and perhaps a group of them will be the ones to conquer Constantinople, as the previously mentioned hadeeth states that 70,000 from the children of Is-haaq (Isac) will invade it. Romans are descendants of Al-‘Ays ibn Is-haaq ibn Ibraaheem Al-Khaleel...” [An-Nihaayah fi Al-Fitan wal-Malaahim]

Allah knows best.