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?
This is explained in chapter 168 of the manga. 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 by 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 do so when she becomes a great chef herself.