According to Mark Feinsand, the Yankees seem to be shopping closer Andrew Miller, but not actively. If a team "overwhelms" them, as Brian Cashman said, then they will make a deal. According to the article, interestingly enough, the Tigers checked in with the Yankees--before eventually acquiring Francisco Rodriguez from the Brewers--but they refused to pay Cashman's asking price of "young pitchers Detroit acquired this summer in deadline deals for Price and Yoenis Cespedes." That probably means something along the lines of Daniel Norris, so understandably it makes sense that Detroit would turn that down.
But that does raise an interesting point: if the Yankees are to trade Miller, young pitching is in the front office's sight. Consider Daniel Norris, for example. Already with 66.2 innings under his belt and just 22 years-old, Norris has a 3.92 ERA in that time and Steamer projections think he'll pitch to a 4.28 ERA in 162 innings next year. I'm a bit more optimistic than that system is--I would imagine the Tigers are as well--and it's reasonable to think he'll be a league average pitcher in 2016. He's also under team control until 2022, which is where a lot of his value resides.
That's all theoretical, obviously, but it's all to say that a pitcher similar to Norris in quality with about two or three years of team control could be reasonable, obviously depending on the circumstances. Another place to look for comparisons are the trades for Craig Kimbrel and Francisco Rodriguez. Rodriguez only netted a lower-level prospect in Javier Betancourt, but Kimbrel brought the Padres Logan Allen, Carlos Asuaje, Javier Guerra, and Manuel Margot. There are obvious caveats in both of these examples because the Red Sox value their minor league depth a bit less than other teams, and the Brewers value salary relief more than a large market team would, but I think these two deals at least point in the general direction of what a trade for Miller would look like.
Miller currently has three years and $27 million remaining on his contract, a number similar to the demands of Joakim Soria and Darren O'Day in free agency, coincidentally. The problem there, of course, is that the latter two only cost money, while Miller would cost both money and your own players. On the other hand, Miller is one of the best relievers in baseball. Miller this past season struck out 100 batters in just 61.2 innings, and he blew just two saves in 38 opportunities. He only has four blown saves in his career. His value will likely never be higher, and the Yankees have Dellin Betances (and those free agent relievers) to fill the void if need be. It's obviously not ideal to deal from an area of serious strength, but it is taking advantage of selling a stock when it's highest.
One team interested is the Diamondbacks, an old trading friend I'd love to see again. In the past Cashman has coaxed Brandon McCarthy, Martin Prado, and Didi Gregorius out of Arizona, and for pretty much nothing in return. Patrick Corbin is the obvious fit here, and Robbie Ray and Chase Anderson are in the mix as well, even though they don't exactly qualify as "overwhelming". Corbin is 26 years-old and missed all of 2014 because of Tommy John surgery, but he did decently well in his return this past season, as he posted an ERA+ of 113 both in 2013 and 2015 over 293.1 innings. I'm pretty sure the Diamondbacks think they can contend and losing Corbin may hurt them as much as Miller helps them, but he'd be my guy.
Another possible fit, one that wasn't mentioned in the initial rumors, is the Angels, and their bullpen posted a pretty poor 101 ERA-; they also missed the postseason by just one game. While I doubt they would part with Garrett Richards, the stalwart of their rotation, both Andrew Heaney and Matt Shoemaker are movable, more likely the latter. Shoemaker had an incredible 3.04 ERA over 136 innings in 2014, but has since regressed to a 4.46 ERA this year. Not only that, but he had a nagging forearm issue near the end of the season that might be a red flag. He's a cheap and controllable starter, but the risks make me think that the front office greatly prefers Heaney, a once-top prospect now proving himself as a major leaguer. As valuable as he is, he was still traded for one season of Howie Kendrick.
Whether it's the Angels, the Diamondbacks, or no one at all, it's clear that Miller has the talent to net the Yankees a relatively young starter, exactly what they would need if they're not planning on signing one of the big free agent starters. Cashman could easily hold on to Miller and it wouldn't bother me at all, but if someone of Corbin's or Heaney's caliber came along, you pull the trigger. The Yankees have increasingly moved their acquisition strategy towards young players that are possibly flawed but have upside, and I expect it to continue.