The Washington Post said on Friday that Miles Harrison, 49, is in hospital after collapsing in shock following the incident in Virginia three days ago. He has been charged with manslaughter, and could be jailed for up to 10 years.
The paper quoted Russian Embassy spokesman Yevgeny Khorishko as saying consular officials are trying to establish whether the child, brought over from Russia three months ago, still had Russian citizenship.
"We are in contact with U.S. officials in this case," he said.
Harrison, the managing director of a real estate consulting firm in the town of Herndon, reportedly left his home on Tuesday with his son Chase strapped into the back seat, and was supposed to take the child to a day care center.
Chase was left in the SUV with tinted windows for several hours outside the office as the temperature in the vehicle rose to around 55 degrees C (130 degrees F). Late in the afternoon, a passerby saw the child and alerted the office receptionist.
The Washington Post quoted a worker in the same building who saw paramedics placing the child's body in a bag as saying: "That's a terrible death . . . with the heat. When I got in my car at 1, my steering wheel, you couldn't touch it."
The incident is likely to renew calls in Russia for tighter controls on adoptions following several high-profile scandals, notably the killing of a two-year-old girl from Siberia by her adoptive mother in the United States. The woman, Peggy Sue Hilt, was sentenced to 25 years in prison in May 2006 for beating the child to death.
Around 120,000 Russian children were adopted both in Russia and abroad in 2007, a 6.4% increase on 2006, according to the Science and Education Ministry.