Since the first Manga, Anzu had established herself as Yugi's first and only friend prior to his friendship with Jonouchi and Honda as well as anything romantic between the two later on. She defended him from Joey when he stole his millenium puzzle and her being harmed in a hostage situation prompted Yugi to transform into Yami out of anger and concern for her.
In the mange volume 10, chapter 80 Mai sends Anzu looking for Yugi. When Anzu finds him she starts talking about how once she broke one of Yugi's games and he just smiled. Thinking that she wanted to speak to Yami Yugi he offers to switch places with him but Anzu stops him.
Prior to the Battle City story arc, Yugi was willing to set up a surprise date for her and Yami regardless of his feelings on the matter.