I think he's about to be a huge beneficiary of the Saints drafting Olave.
Callaway, in my mind, is destined for the slot. Physically, he does not have any stand-out qualities (he's not short but isn't extremely tall, doesn't have a lot of bulk, isn't very twitchy and does not possess the separation gear to consistently get open outside). But he is an overachiever, and one place those guys can go and really succeed in the NFL is the slot.
Think Lance Moore. He was a guy who didn't have a blazing 40, really didn't have a ton of natural quickness (athletically). Now he had great mental agility--awareness, anticipation--those are the guys you often hear being talked about as "faster than their time (their 40, their cone drill)". If you put Moore outside and asked him to do what Callaway was asked to do last year (to be a #1 WR), he would have struggled much more.
The reason the slot fits these guys is because it instantly puts them at an advantage--especially if you have outside guys who are demanding a defense's best cover players. Then there is the spatial advantage: a slot WR has a 2-way go, every play, and that stresses the a nickel in man or the underneath coverage in zone. You can't squeeze them to the sideline, and it's much harder to reroute at the LOS. A WR can be a lot less athletic if he understands stems and manipulating space from the slot. He becomes one of those "sneaky" slot WRs.
With the Saints essentially adding 2 1,000-yard receivers to the roster this season (since MT was injured all last season), Callaway will have the opportunity to slide into a more complementary role. I don't think he's Lance Moore yet, but he has that mental agility that makes up for some of what he lacks physically. If he learns to command and manipulate space, continues to refine his route running, and gains a little more veteran savvy, I think he is the Saints answer at slot WR.
The odd man out, IMO, is Tre'Quan Smith. I don't mean that the Saints release him (he's not expensive, has great speed and run blocking stature, and will provide crucial depth outside), but I definitely see his share of snaps decreasing. With what I know and have seen of the Saints WRs thus far, I think Callaway is the #3 next season and becomes much more of a slot WR specialist.