In the anime, Nakiri is waiting for Jōichirō Yukihira to come, why is that? Is it possible that Nakiri is related to Soma? Because we don't know anything about their mothers?
It's because Joichiro is like an influence to Erina and he is really dear to her and also he agreed to taste her cooking when she becomes a good chef. And also no, Yukihira Soma and Erina Nakiri are not relatives.
Ok I have an answer to the question to your comment and question. it is stated in the wiki that At the age of 28, Jōichirō was summoned to the Nakiri Mansion by Senzaemon to discuss a matter of importance. During his visit, he met a young Erina Nakiri. Though Senzaemon told her to go back to her room so he could continue to discuss something with Jōichirō, Erina's stomach growled. Jōichirō immediately prepared a dish just for her and with a single bite, Erina was completely enthralled not just by the unique taste of his dish, but also Jōichirō's charm. This event became a turning point in Erina's life and she requested for a photo of the two together, a notion Jōichirō happily obliged. She also asked for his name and if he would ever taste her dishes. Jōichirō promised he would only when she became a great chef herself