The fact that Trump didn’t bring up the idea himself means that he wasn’t thinking about it, and the fact that he “waffled” means that he doesn’t really want to do it.
As Jesse Kelly points out to his audience, the right running mate is going to be somebody you don’t like (and he doesn’t like either). It’s not going to be somebody who’s a copy of Trump and doesn’t bring in votes that Trump doesn’t already have. It’s going to be somebody different from Trump, somebody who does bring in votes that Trump otherwise wouldn’t have received. Hate Pence all you like, but he was the right running mate for Trump. Kari Lake definitely wouldn’t be.
That's quite an assumption.
The president may not have a list at this point, and even if he did he most certainly wouldn't want to comment on it at this time.
Pretty standard approach.