Can it be done? Absolutely! Does it make a good suppressor host? Maybe not so much.
It's very much like trying to suppress an AK. While it's easy to screw a can onto the end of the barrel, you still get a lot of gas dumping out of the gas port as the gun cycles. As this gas is not routed through the silencer, it still makes a "bang" as it is released and expands rapidly. True, the sound is cut down a fair amount, but it's still never going to be a "quiet" silencer host.
Next up, the gun is designed to cycle with "full power" ammo. It needs a lot of gas volume, not just pressure. That is why the slower powders work better, and the faster powders generally don't work so well. Unfortunately, when loading for suppressed applications, you typically want to use a faster powder to produce less gas volume so there is less for the silencer to have to slow and cool. So loading to cycle vs. loading for quiet will be at odds. You will have best luck using heavy bullets, 180 or 200 gr. for the .357 Mag. I am not aware of any jacketed bullets heavier than 200 gr. in that caliber.
Do you reload? Because that is likely the only way to find a subsonic load that will cycle the gun. Or you could just shoot full-powered supersonic ammo. Again, not as quiet, but it takes care of the cycling issue. And actually, the gun would cycle more reliably with a supporessor in place, due to the increased backpressure.
And then of course, there is where all that backpressure goes. Usually right into the shooter's face. Shooting suppressed you almost want goggles or a scuba snorkle. Some powders are worse at this than others.
Next up, you're going to need to find a 10" barrel to have cut back and threaded. And if you read some of the recent threads on this forum, you may notice those are becoming difficult to source lately. Or you may be able to have someone cut internal threads into the end of a 6" barrel. You would have to be careful that they didn't get into the gas tube under the barrel bore. But I think there should be little danger of that wiht the .357 barrel. I have never seen it done with ID threads on a Desert Eagle, but I think it would look cleaner, and you would retain your front sight.
Oh yeah, and depending on what can you use, you may end up wtih a 2-foot-long "pistol".
Not trying to discourage you. I just want you to know what you're potentially getting in to.
So having said all of that, I bought a 10" .44 Mag back in '09 with the intent of doing just what you are proposing. In spite of its limitations, I think it turned out pretty well. The thing is heavy and awkward, but it's still a lot of fun.
Hang on, more to come shortly...