A Russian official reportedly claimed the American had volunteered to fight alongside Ukrainian forces.
That account has not been confirmed by U.S. officials.
CBS News reported that government officials were not releasing the man's name out of respect for his family.
According to Newsweek, at least 6 Americans have been killed in Ukraine.
The conflict in Ukraine has been going on for six months and shows no signs of stopping. Russian President Vladimir Putin on Thursday ordered an increase of more than 100,000 troops to prepare to fight in Ukraine.