At the beginning of the series, Koneko was the only member of the club who openly disliked Issei due to his perverted and lecherous nature, but she did admit that he was a hard worker and very determined. In Volume 5, Koneko started to develop feelings of love for him after Issei helped her overcome her fears of using Senjutsu after Issei told her that he was not afraid of her and would stop her if she ever went out of control, giving Koneko the courage to accept her true self.
Afterwards, she began to sit on Issei's lap, marking it as her territory, and began competing with the other girls for his affection, often getting jealous whenever he gets close to another girl, particularly Ravel. During a Senjutsu healing session with Issei in Volume 7, she tearfully asks him to never use Juggernaut Drive again and states that she will keep doing these sessions for the rest of her life if that's what it will take to heal the life energy he lost, showing how much she loves and cares about him. However, she still insults him whenever his perverted side emerges.
Koneko's feelings for Issei kept growing until it reached its pinnacle when it forced her into mating season and chose him as her partner, which she was only brought out of by her sister Kuroka. In Volume 11 she proposed to Issei whilst being attacked by the Hero Faction as well as grim reapers, in which Issei agrees to marry her as long as she's able to grow in height and bust. She was in shock after Issei's 'death', trying her best to hold in her feelings until she breaks down in tears after being scolded by Ravel. She was overjoyed upon hearing that he was still alive and embraced him when he returned. She is determined to marry him in the future, and will sometimes say that she will be Issei's bride one day.
Koneko is very loyal to Rias and cares a lot for her after Rias took her in and helped her get out of her depression after her sister, Kuroka, abandoned her.
Koneko has a friendly/hostile relationship due to the fact she is a Nekomata and Ravel is a phoenix, alluding to the natural rivalry between cats and birds. Koneko sees Ravel as her main rival for Issei's affection, openly competing against her for his love. In Volume 10, while visiting the Underworld with the rest of the club with the exception of Ravel, she stays attached to Issei as she believes that Ravel will take Issei away from her. However, they are shown to get along and become more friendly with each other as time goes on, usually only showing hostility to one another when it involves Issei, such as in Volume 14, where the two are shown to be fighting over the spot on Issei's lap.
The two appear to have a positive relationship, as in Volume 3, Koneko was willing to disobey Rias's orders to help him find closure with the events of his past. Koneko sees Kiba more as a brother and even stated in Volume 3 of the light novels that she would "get lonely" if Kiba disappears, this would mean that Koneko really cares about Kiba.
Koneko, being one of the three 1st year members of the Occult Research Club, gets along with Gasper. However, she does seem to enjoy frightening him, occasionally being spotted in the series chasing Gasper while holding garlic, something that he naturally fears because of his natures as a vampire. Nevertheless, she still cares deeply for him and is extremely protective of him.
Sirzechs was the one who rescued Koneko from being executed after Koneko's sister, Kuroka, killed her previous master and left her in Rias' care.
She cares for her sister but she is angry at her for what she did to her old master even though she was right for doing this. Koneko had to live a tough life because of her, but Kuroka loves her greatly, and Kuroka proved it when the Hero Faction attacked and she took a hit for Koneko. Issei told Koneko that she is a good person, although a "naughty cat", and is willing to punish her if she did anything funny to Koneko. Koneko is thinking about re-establishing her relationship with her and thanks Issei for the courage he gave her.