The friendship between Kara and Lena seems to go way deeper than the two of them being platonic friends. Nevertheless, they’ve never actually gone any further than sharing a friendship with each other. On top of that, they’ve both only dated male partners in the past.
The writers of the show were very careful not to take things too far while also creating a very slim chance for viewers to remain hopeful about the possible ship between Kara and Lena. To fans of the show, this romantic union has been labeled “Supercorp.” Hoping Kara and Lena finally link up has been an ongoing wish among Supergirl fans for years now. It doesn’t seem like something that will ever come to fruition though.