Probable
Josh Collmenter
This is Collmenter's fourth season, mostly bouncing between the bullpen and the rotation - he was purely a relieve last year, but so far, he has 51 starts and 78 appearance in relief. It'd be nice if the team could provide him with some stability, but he's just such a Swiss Army knife, and that's part of his value. However, he has done little at this point to pitch his way out of a rotation spot.
Wade Miley
Miley is becoming our own iron man. Since the start of 2012, his 81 starts are good for the top 10 in all baseball, and that figure is twenty more (and still climbing) than the next most-reliable Diamondback, Trevor Cahill. His performance over that time has been solid rather than great (106 ERA+), but there's something to be said for a pitcher who just takes the ball every fifth day. Like Bronson Arroyo. Er, never mind.
Likely
Trevor Cahill
The team has made it clear that Cahill will be back with the team sometime. Though if he stopped walking people in the minor-leagues,. that would probably help speed things up: 15 in 26.1 innings so far. He's under team control for the next three years: while the options aren't cheap ($38.5m in total), if Cahill can get back to career average form (ERA+ 103) that wouldn't be bad value, the way free-agent costs have gone. But that's an "if".
Patrick Corbin
Obviously, this depends entirely on Corbin being able to make a smooth transition back from the Tommy John surgery he had at the end of March. Generally, there's a 12-month recovery, but it's worth noting it may take some time past that for a pitcher to regain full effectiveness. For example, when Adam Wainwright came back in 2012, his April ERA was 7.32, and it was 4.09 for May-June. After that, however, it was 3.18.
Possible
Chase Anderson
Of the unexpected arrivals in the Diamondbacks rotation this season, Anderson has put up the best ERA, with a solid 3.64 ERA through ten appearances. As a yardstick, Miley had a 3.83 ERA through his first ten games, though he was two years younger. Anderson has been a bit prone to the home-run, allowing nine in 54.1 innings, and improving his ground-ball rate beyond the current 38.8% would help (NL avg = 46.6%)
Mike Bolsinger
However, if you prefer the peripheral stats as predictor of future performance, Bolsinger might be your man, as his major-league FIP and xFIP are both better than Anderson's, at 3.89 and 3.33 respectively. They're more or less the same age - Mike is two months younger, but there's very little to choose between them over the larger sample-size of their minor work. Bolsinger has a 3.30 ERA in 425.2 IP, Anderson is at 3.44 over 398 IP.
Archie Bradley
In spring, it seemed more a question of when, not if, Bradley would join our rotation. However, injury has limited him to 9 starts, and Bradley's performance hasn't been what we hoped either, with a 3.95 ERA and 22 walls in only 41 innings. With the team well out of contention, there's little point in starting his service clock, so I suspect we'll see no more than a token September call-up. But should be in the mix again come spring.
Fringe candidates
These would include the likes of Randall Delgado and new arrival Vidal Nuno. Delgado didn't exactly impress in his temporary transition to the rotation early in the season, and if Collmenter sticks in the rotation, will probably find himself remaining as a long-man in the bullpen. While Nuño certainly impressed with his Diamondbacks debut, obviously, seven shutout innings will be the exception, rather than the norm. Still, if he does continue to transition well to the National League, he should be in the conversation as a far as a 2015 spot goes.
New arrivals?
Going into this winter, our rotation probably seems weaker than the one we had at the same point last year - and that led to the pursuit of Masahiro Tanaka, and the eventual signing of Bronson Arroyo. However, the purse strings may not be as flexible this off-season, unless we can drop some big contracts. Deals coming off the books include Eric Chavez ($3.5m) and J.J. Putz ($7m), but that will be eaten up in increases for Trevor Cahill (+$4.3 million), Paul Goldschmidt and Miguel Montero (+$2.0 million each). plus various arb-eligible players. With team payroll already at a record level, and underwhelming results, Ken Kendrick and the other owners may not want to be tapped further.