So I saw the solicit for Supergirl coming up featuring Jason, and I also recently read an interview stating that Supergirl would be featuring a new love interest for Kara. I'll post the solicit bellow for reference, but I was thinking with their previous encounter being mostly nice (Superman/Batman annual #1), and with Jason appearing in Supergirl, I think it could be possible that he is her new love interest.
Here is the link to the article:
Here is the solicit:
“SUPERMAN: DOOMED AFTERMATH”! In the waked of the DOOMED storyline, the ALIEN SYNDICATE looks to re-establish it’s foothold on Earth. But the venom powered Red Hood looks for even more muscle in Kara as they go head to head with the scum and villainy of the galaxy. Plus: an ending that will set Kara on a new course!