You realize Miller is turning 34 in a few months, is an upcoming UFA and doesn't exactly have much of a market? Its not like he's 28 and signed for another 5 seasons.
The thing about Miller is his market is based on a lot of factors, as well as who is in or out of the playoffs come the trade deadline.
The only logical sure thing team is St.Louis. Even if they are the only team in the bidding, they don't hold all the cards. This is supposed to be St.Louis' year. If they refused to bring in Ryan Miller at the trade deadline due to haggling, and then end up losing in the playoffs due to a lack of elite goaltending, they will end up facing immense scrutiny.
If Buffalo refuses to move Miller, they'll also face the same thing, but under a much less heavy context. "You let Miller walk without getting us a late first round pick in a bad draft" is a lot less damning than "Your hubris cost us a Stanley Cup".
If everything goes right for Buffalo, they could potentially have three possible teams to move Miller to. St.Louis, Minnesota, and Washington.
Josh Harding has been great, but unfortunately health issues might leave him unable to play, while Kuemper has been good he is still a rookie who has only played 21 games in the NHL to date. Backstrom has not been good.
Capitals are a fringe playoff team with some times shaky goaltending. If they convince themselves that an elite goaltender would make their high scoring team deadly come the playoffs, they are also a possible destination for Ryan Miller.