Source: Tafsir al-Ahlam al-Kabir (Ibn Sirin)
The elephant is a huge, tyrannical foreign king. Riding an elephant indicates gaining authority or marrying a woman of great origin. Killing an elephant is conquering a king or a country.
Source: Ta'tir al-Anam fi Ta'bir al-Manam (Al-Nabulsi)
The elephant indicates a blessed man or a king. Whoever sees himself speaking to an elephant will receive goodness from a ruler. Whoever sees a dead elephant, a great king has died in that land.
Source: Al-Isharat fi Ilm al-Ibarat (Ibn Shahin)
The elephant is interpreted as a man of great stature or a king. Speaking to an elephant is receiving a blessing from the ruler. Whoever sees himself fleeing from an elephant is fleeing from the ruler.