There are few scenes in which Saionji is actually shown interacting with Nanami. As the younger sister of his best friend, it would probably be safe to say that Saionji views Nanami as a sort of "younger sister" as well, albeit a rather annoying one. The two of them don't seem to mind each other, but neither of them pays much attention to the other, either. There are several episodes in which the two of them play off each other to provide comic relief to the series (eggs, anyone?)

Strangely enough, Saionji's relationship with Touga is never a big issue with Nanami. Saionji is the only character in the entire series who Nanami allows to be close with Touga without her trying to interfere. Perhaps this is because Saionji and Touga have been friends for so long that she doesn't consider him a threat, or maybe even considers him part of the household. Whatever the case, Nanami must be used to seeing Saionji around.

I've seen several fanfiction writers pick up the Saionji/Nanami relationship as a possible romantic one in the future of the characters' lives, and I think that's a very fascinating and entirely plausible concept. There are definitely no sparks of love flying between them during the series, however.

Nanami is the only character who calls Saionji by his given name, "Kyouichi."