OK, if you want to put a 2011-2014 Mustang 3.7L V6 into a SN95, it will fit, but their are a lot if issues. Basically, since the 5.0L Coyote fits, the 3.7L V6 will as well.
First, you need to decide what trans mission you want to use. 6R80 auto or the 2011-2014 manual trans. Because the rear face of block (RFB) is unique to this engine (and the 3.5L Ecoboost) you trans choices are limited. I understand you can buy an aftermarket bellhousing to adapt to a T5 as well. (5.0L Coyote uses same RFB as all Mod motors, so trans choice is not an issue.)
The only control system you can use is the Ford Factory PCM and wiring found in the 2011-2014 Mustang if you want to use the 6R80. It is a very complex system and you will need to have the PATS key as well as the 2011-2014 Mustang instrument cluster as that is where the PATS module resides. (Ford Racing sells a Controls PAK for the 5.0L Coyote, but not the 3.7L V6.)
There is no power steering pump on the 3.7L, it uses Electric Steering. Aftermarket sells pump and mounts for the the 5.0L Coyote, but not so for the 3.7L V6.)
Can it be done? You bet! Will it be easy or affordable? No. When you get done, you could have likely bought a used 2011 Mustang V6 for the same price.
Sorry, it would make a fast fun SN95 with some great gas miles, way better than the old 3.8L V6!
OK, it has been over one year, so here is some updated info.
HP Tuners can now turn off the PATS system in 2011-2014 Ford PCMs, so this greatly simplifies your wiring system and you now do not haved to use the 2011-2014 instrument cluster as part of your swap kit. (PATS is in the cluster on 2011-2014 mustangs).
AJE Racing now sells motor mounts for the 3.7L V6 that allow you to bolt-in the engine when you use the AJE Racing K-member.
All the other issues raised above still need to be overcome. I highly recommend that anyone attempting such a swap start with a wrecked 2011-2014 mustang that runs and lot-drives so that you have a powertrain that you know runs and you have every 2011-2014 part you need to transplant that powertrain into another vehicle.