This could be considered a trick question, since your question does not stipulate whether you mean Ali or Hassan's actual father, Baba. In either case, Hassan seems to worship them both. He no doubt appreciates Ali, the man he calls father, and the man who stood by him and took care of him after the desertion by the mother Sanaubar. In Hassan, Ali "had found his joy, his antidote" to the tormenters who constantly reminded him of his physical limitations. Hassan and Ali share their work together, cleaning Baba's house and buying fruits and vegetables from the market each day. Hassan is eventually able to confide to Ali about Assef's rape and Amir's betrayal. When it comes time for the two to leave Baba's household, Hassan faithfully follows him without objection. And when Hassan's wife becomes pregnant, he prays "for a boy to carry on my father's name."
Hassan also admires Baba and he looks forward to the birthday presents he receives each year. Though Hassan never discovers Baba's secret--that he is actually Hassan's father--he loves Baba: Hassan and his wife pack up and leave their own home to return with Rahim Khan to take care of Baba's house, returning it to its previous glory in the hope that Amir will one day return. When Rahim Khan tells him of Baba's death,
... Hassan buried his face in his hands and broke into tears. He wept like a child for the rest of that night. (Chapter Sixteen)
Hassan ironically tells Rahim that "Agha sahib was like my second father..." As for Rahim Khan, Hassan is so happy to see him visit his little hut outside Bamiyan,
I had to make him stop kissing my hands. (Chapter Sixteen)
Hassan and Farzana gladly join Rahim and return to Baba's home, understanding that Rahim can no longer manage the house on his own. In Hassan's letters to Amir, he calls Rahim a "dear man," and reveals to Amir that little Sohrab "adores" him as well.