Newsweek magazine said it had heard a tape of a recent talk given by Antonin Scalia in which he made these comments.
The report comes as the court prepares to hear a challenge by a Guantanamo detainee against US military tribunals.
The case is considered an important test of the Bush administration's handling of its war on terror.
Lawyers for Salim Ahmed Hamdan - Osama Bin Laden's former driver - will argue that President George W Bush does not have the constitutional right to order these military trials.
The US government has urged the Supreme Court to dismiss the case.
'Hypocritical'
In a speech to Swiss law students at the University of Freiburg on 8 March, Justice Scalia dismissed the idea that detainees had rights under the US constitution or international conventions, Newsweek reported.
"War is war, and it has never been the case that when you captured a combatant you have to give them a jury trial in your civil courts," he is quoted as saying.
"Give me a break."
Asked whether Guantanamo detainees have any rights under international conventions, Justice Scalia reportedly answered:
"If he was captured by my army on a battlefield, that is where he belongs.
"I had a son (Matthew Scalia) on that battlefield and they were shooting at my son and I'm not about to give this man who was captured in a war a full jury trial. I mean it's crazy."
Mr Scalia is also quoted as saying he was "astounded" at the "hypocritical" reaction in Europe to Guantanamo.
Legal experts quoted by Newsweek said Mr Scalia's comments could compromise his position in the Hamdan case, even though he did not refer directly to it.
Eight judges are expected to start hearings in the Hamdan case on Tuesday. Chief Justice John Roberts has decided not to take part in the hearings because he ruled on the case while he was an appeals court judge.
About 14 out of the estimated 490 Guantanamo detainees have been deemed eligible for hearings under the commissions.
