Is suspension stock height?
On my 94 K2500, stock suspension, I put 265/75/16 Toyo M55 tires on and had to do some trimming. The rims were not stock offset so that is where my problems stemmed from. Due to the increased offset (not sure how much, didn't measure) the tire did contact the lower inner edge of the bumper.
I'm assuming the pickup you are wanting to put these tires on is the one in your avatar. Here's some pics of my pickup. Look at the tire and bumper to see how far out the tire sets. I don't see any fender flares in your avatar and my first pic is with a fender flare. The second pic is without a fender flare. Third pic is farther back and showing both sides. Sorry for the crooked pics. I was on a slope when I took the pics.
I was going to start my pickup, turn the steering wheel a bit to show you how close the tire comes to the bumper. But I haven't started it in almost a week and I forgot and left the GPS plugged in. After the glowplugs cycled the batteries didn't quite have enough oompf to turn it over fast enough to fire. I put the charger on it for overnight so tomorrow I'll be able to get more pics.
Anyhow, If you have a wide rim with stock offset I'm thinking you'll have more clearance problems than I did. With my greater than stock offset, as the steering pivots the tire, the outer corner of the tire tread is actually put into closer contact with the rearmost edge of the bumper. It's kind of hard to explain, but it's like the farther the rim/tire combo sets out from the ball joints the greater the arc of the circle becomes as the tire pivots to turn the vehicle. As this arc becomes larger the tire comes closer to the bumper, or other body parts.
You may have to mount a tire, put it on the front and see just how bad the clearance problems will be.
Don