Pursued by God? - Yes, God has ...

From Compendium - Catechism of the Catholic Church:

2. Why does man have a desire for God?
God himself, in creating man in his own image, has written upon his heart the desire to see him. Even if this desire is often ignored, God never ceases to draw man to himself because only in God will he find and live the fullness of truth and happiness for which he never stops searching. By nature and by vocation, therefore, man is a religious being, capable of entering into communion with God. This intimate and vital bond with God confers on man his fundamental dignity.