Source: The Great Interpretation of Dreams (Ibn Sirin)
Chasing in a dream indicates dispute and striving for a matter. If the chaser wins, he achieves his goal. If he is defeated, he loses.
Source: Perfuming Humanity in the Expression of Dreams (Al-Nabulsi)
Chasing indicates fear and hardship. Whoever sees himself chasing an enemy will triumph over him.
Source: Signs in the Science of Expressions (Ibn Shaheen)
Chasing is interpreted as worry. Whoever sees himself chasing is in worry.