The United States maintains a naval base at Guantanamo Bay, Cuba, leased (wink wink nudge nudge) from the Cuban government in 1903 for an indefinite period for use as a 'coaling and naval station'. It now also houses a military prison. The U.S. government houses non-military 'terrorists' there because, the argument goes, the Constitution, especially the 5th amendment (self-incrimination), the 6th amendment (speedy trial, jury of peers, cross-examination of witnesses), and the 8th amendment (cruel and unusual punishment), doesn't apply outside the United States. Really?
Let's take a look at some of those amendments.
No person shall be held to answer for a capital, or otherwise infamous crime, unless on a presentment or indictment of a Grand Jury, except in cases arising in the land or naval forces, or in the Militia, when in actual service in time of War or public danger; nor shall any person be subject for the same offence to be twice put in jeopardy of life or limb; nor shall be compelled in any criminal case to be a witness against himself, nor be deprived of life, liberty, or property, without due process of law; nor shall private property be taken for public use, without just compensation.
Note that nowhere therein does it say anything like 'citizen'. It says 'person', the implication being that the government (who else deals with capital offenses and criminal cases?) is precluded from doing any of these things to anybody, citizen or not.
In all criminal prosecutions, the accused shall enjoy the right to a speedy and public trial, by an impartial jury of the State and district wherein the crime shall have been committed, which district shall have been previously ascertained by law, and to be informed of the nature and cause of the accusation; to be confronted with the witnesses against him; to have compulsory process for obtaining witnesses in his favor, and to have the Assistance of Counsel for his defence.
'The accused'. 'All criminal prosecutions'. Again, no hint that this applies only to citizens or that it applies only within the borders of the country — 'all criminal prosecutions'. This is not a right being doled out, this is an instruction to the government: follow this procedure. All the time. Every case.
Excessive bail shall not be required, nor excessive fines imposed, nor cruel and unusual punishments inflicted.
...except for foreigners being held at Guantanamo Bay... Nope, it doesn't say that. Again, it's a plain instruction, applicable to everyone, everywhere, all the time, not restricted as to person, place, or time.
So the next time someone says "We can't close Gitmo! Then we'd have to treat them like citizens and give them regular trials!" you can explain to them that we have to give them regular trials now because the Constitution is blind to the fact that these people aren't citizens and aren't here.
Of course, first you're going to have to overcome the barrier that the American people are blind to their own Constitution.