Always go to the source:
Chapter 55 - Phantom Gun Syndrome
Miller,” said Brown, from his enormous white leather recliner, across ten feet of off-white shag carpet. “Your name is David Miller. Same birthday, same age, same place of birth.”
They were in a Gulfstream jet on a runway at Ronald Reagan. Milgrim had his own white leather recliner. He hadn’t been to this airport since it had been National. Across a bridge from Georgetown. He knew this was a Gulfstream because there was an elaborately engraved brass plate that said “Gulfstream II” on the high-gloss wooden surround of the window beside his chair. Bird’s-eye maple, he thought, but too shiny, like the trim in a limo that was really trying. There was a lot of that in this cabin. And a lot of white leather, polished brass, and off-white shag. “David Miller,” he repeated.
“You live in New York. You’re a translator. Russian.”
“Your passport,” said Brown, holding one up, navy blue with pale gold trim, “is American. David Miller. David Miller is not a junkie. David Miller, upon entering Canada, will neither be in possession of nor under the influence of drugs.” He checked his watch. He was wearing the gray suit and a white shirt again. “How many of those pills are you holding?”
Milgrim is born the same place as David Miller, the fictive owner of the fake American passport Milgrim is forced to use for his journey to Canada. If said David Miller was born anywhere other than the US, I'm sure it would have been mentioned.
Thus my conclusion - American