If they were for a disc brake Mustang they will. But you need to do some research to tell what ones they are. If you have a picture of the back side I may be able to tell. But it needs to be a good, clear picture.
That is a Mercury Styled Steel Wheel, used on Cougars and Comets. Someone has but a Mustang center cap on it.
'67s will not fit '68 and later disc brakes - '68s (chrome) and later (argent) will. You can look for a groove around the rim on the backside of the wheel (to clear the discs) - that can be a clue that they are disc brake wheels.
- Phillip
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Thanks they are on Facebook marketplace in Seattle for a steal of a price. There is a picture of the backside and off a 66 Mustang.
That’s a '67 wheel. You will need a spacer to fit '68 and new disc brakes.
Sorry if I’m covering ground you already know - that wheel that you posted was not original equipment on any Mustangs - it is a Mercury wheel.
The Mercury Style Steel Wheels were chrome with beauty rings in '67 and '68. The wheels from those years look very similar but are different. Along with the extra clearance for the larger disc brakes in '68 the openings are also a little smaller for added strength.
Starting in '69 the wheels were painted an argent metallic grey with chrome or stainless (can’t remember now) inserts. If you want to be more correct, these are the wheels that would have come on your Cougar if so ordered.
- Phillip
On Ford/Mustang styled steel wheels, the holes are in the raised spokes, not between them as on the mercury wheels
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There are replicas of these Mercury Styled Steel Wheels (which are often referred to as the “flat Five”. Most are 15". The steel 15" replica being sold everywhere now is terrible; there’s only one company still making them, and the equipment and/or quality control are very poor. They’re not well balanced, nor concentric.
Legendary Wheels is making an aluminum version (LW67) that is very high quality - I bought a set for myself to replace the rusted out Magnum 500s my car’s worn for so many years.
Anyone else think these bear a striking resemblance to the original “Hot Wheels” mags on the toy cars from 1968? I may have to get some red line tires eventually… 
Yep - best factory mag of the original Pony Car/Muscle Car age IMHO. Inspired by the Cragar SS I’m sure, but I love the Mercury’s crisp edges and the cut-outs.
I’ve seen more than a few vintage Mustangs running them.
- Phillip
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Any ideas on how thick a spacer I would need and would it look odd with spacers in the front and none in the back. Thanks for the responses.
That’s actually not a good idea. Sticking the wheels out farther like that, changing the backspacing, leads to weird handling, extra leverage on your bearings, and other undesirable (or even dangerous) traits.
I wouldn’t do it.
I ran the '65 Mustang GT wheels on my "68 Cougar with disc brakes and had no issues with clearance. It is likely the wheels are reproductions, not originals. I’d be interested to get in touch with whoever ends up with the wheels, because I have the Cougar centers and would like to swap them back to the Mustang ones. Would be great to find someone to do a direct swap.