Having an interest in something with

気(き)がある means to have an interest or inclination. When said about a person, it often hints at romantic interest without stating it directly.

Dictionary Definition

1 意志(いし)・意欲(いよく)がある。

2 興味(きょうみ)や関心(かんしん)がある。特(とく)に、恋(こ)い慕(した)う気持(きも)ちがある。

1) There is intent/desire.

2) There is interest (in something). Particularly, a feeling of yearning.

Goo Dictionary

Examples

Interested in him with 気がある

Manga panel from ふらいんぐうぃっち showing example of Interested in him with 気がある.
ふらいんぐうぃっち » Volume 5 » Page 57

Makoto and her family head out on a trip to the river. When they stop to pick up Kei’s friend Nao, Akane greets her with, “Howdy, Kei’s girlfriend!” Nao tells her she’s wrong.

圭(けい):
「よっオレのカノジョ」
“Yo, my girlfriend.”
なお:
「やめてよ」
“Stop that!”
茜(あかね):
「と言(い)いつつ気(き)があったりするんでしょ?」
“Although you say that, you're interested in him, aren't you?”