I think Sasuke did not have a personal relationship to Izumi, and I’m skeptical if Sasuke even met her at all aside from glimpsing each other in the Uchiha compound occasionally.

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Izumi drifted in and out of Itachi's life rather than the two having a steady friendship. It appears Itachi's family was not well-acquainted with Izumi, since Fugaku did not know Izumi well when he talked to her for seemingly the first time in Itachi’s Story: Midnight shortly before the massacre. Itachi and Izumi’s friendship seemed detached from Sasuke’s life. Most probable is that Itachi never mentioned Izumi to Sasuke, and young Sasuke probably was oblivious that Izumi had any relationship to Itachi.

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Tobi told Sasuke about Itachi's lover, so whether Sasuke knew which girl it was that Tobi spoke of is uncertain. Perhaps Sasuke knew Itachi's lover was Izumi, though I doubt it, seeing as how Fugaku only realized Izumi’s feelings for his son very shortly before the massacre, and that’s the type of subject that would escape a 7-year-old’s notice. I don't think Sasuke knew that anyone romantically loved his brother until Tobi told him about it. And even then, it’s possible that Sasuke never trusted or believed Tobi’s claim that his older brother had a lover.

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There are only a couple scenes with Izumi and Sasuke. One is where Itachi brought Izumi to safety during the Ninetails’ attack on Konoha, Izumi and Sasuke were in the same vicinity, but no interaction passed between them.

 

The second was when Izumi she mistakes baby Sasuke for a little girl. Even then that scene revolved around Sasuke’s relationship to Itachi, as even as a baby Sasuke is evidently obsessed with Itachi, seeing as how Sasuke cries and screams and pushes Izumi away, but laughs and giggles once he is safely back in Itachi’s arms, much to Izumi’s irritated ire.

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In any case, Izumi didn’t seem at all involved with Itachi’s younger brother, as she was more interested in her relationship with Itachi himself and uninvolved with Itachi’s family, a stark contrast to Shisui, who took Itachi and Sasuke as a bit of a package deal with Itachi. Sasuke and Izumi appeared to have lived lives entirely detached from each other.