My car was doing the same thing and the problem was the coil spring seat. It is the part that the front coil spring sits in and it bolts to the lower control arm. The bushing in the center of the seat had worn and slipped out of place causing the suspension to roll forward. This made the tire contact the fender toward the front of the fender. I guess it could do the same to the rear also. I have 17 inch rims and they clear fine. But I guess the wrong tire size could be a simple problem, but if only one side is rubbing check out the spring seat. Only a $20 part, but you have to remove the spring to replace it. Good Luck.
Ryan - Marysville, OH
1965 Fastback Mustang (GT350 clone)