Aoba is frequently seen hanging out with her and Mairu, much to the jealousy of his underlings, and behaves in a much friendlier manner towards them than anyone else. It is implied that Kururi may have a crush on Aoba since he saved her from some bullies earlier but she denies this when it was brought up. Aoba is unsure about how he feels about the Orihara twins. He is shown to care about them to a certain extent as he told his gang to refrain from attacking them should they see them in the street. In volume 09 he expresses his fear of being alone and without any friends (much like Izaya) which would mean that he is growing tired of his rather isolated lifestyle.
These feelings haven't been addressed from Kururi's perspective however, Aoba has stated his own feelings on the situation. While he doesn't completely reciprocate Kururi's feelings for him, he does see her and her sister as friends and wishes to stay connected to them in some way so as to avoid being a complete recluse like their brother.
In one point of light novel volume 9, they are hanging out at the pool in Raira and Kururi decides to play a prank on Aoba by pressing a beachball up against his back and hugging him from behind. Aoba (who wasn't paying attention) thinks it's Kururi pressing her chest against him only to realize their prank too late. He is subsequently dragged into the pool along with them.
In Durarara!! SH, Aoba claims that he would have Kururi as his girlfriend rather than Mairu.
Aoba is not sure if he likes her, though he has admitted from time to time that he prefers her over Mairu.