It's probably a good thing the media didn't go out of its way to cover gossip.
That specific rumor is based on the idea that Sinema wants to run for President, which is odd for someone who doesn't do interviews with national media, or even alternative media.
It seems to be based on the idea that if a politician does something that partisan writers don't like, the obvious explanation is that there's some kind of ulterior motive, because no one would need a motive to vote the way you want them to, and no one would profit by impressing people like you.