Is it valid to set the intention of nazar without verbalizing it?
Imam al-Nawawi stated that the most sahih opinion in this issue of which has been agreed by Syafi’iyyah scholars is that the nazar is invalid except it is verbalized in words and it is not valid if it is just an intention in a person’s heart.  Imam Jalaluddin al-Suyuti when explaining the methodology of al-umur bi maqasidiha stated that a nazar through intention in one’s heart isn’t considered as nazar. 
To conclude, it is only be considered as nazar and obligatory to be fulfilled if it is verbalized in words. If it is just an intention in one’s heart, then it isn’t considered as nazar.