Unless your state has a hunting season for wolf, it's illegal...to kill it for killing animals only works if you can prove it's killing your livestock, which wild deer don't count as (unless your property is commissioned as a controlled hunting ranch), in which case you would have to get permission from the state by proving that it's harming your livestock.

All that said, I took three coyotes this year that fit the bill you're describing, narrow muzzle, RED coat, huge body...they're coyotes, we don't have wolves of any kind here in KS...I sent a pic into KDWP and they said it was probably a second generation cross breed, i.e. a coyote bitch got bred by a large domestic dog, and then one of her kits got bred by or bred a coyote...first gen's tend not to look so much like wolves/coyotes, but second gen's get the size of the dog, and the looks of the yotes.