According to the Wall Street Journal, the men want to recapture towns and villages overtaken by the extremists.
The US newspaper also says many Christians believe both government and Kurdish forces abandoned them when Islamic State attacked them last year.
The Islamic extremists have displaced 150,000 Iraqi Christians during its campaign, according to faith leaders in the country.
The report suggests those taking up arms are hoping America will fund their military training and equipment, and that several Americans were helping train the young men with a non-profit organisation they refused to name.
American politicians approved the National Defense Authorisation Act in December, which says non-governmental armed forces fighting against Islamic State could receive up to $1.6bn of funding.
The Act specifically names the Nineveh Plains, an area of northern Iraq where a significant amount of Christians and other religious minorities live, and the place where the men will be training.
The Iraqi men receiving training are currently relying on donations and their own money.
Local Christian politicians have campaigned for the last ten years to arm and train a Christian regional guard, but this was resisted by Iraqi authorities.
The Assyrian Democratic Movement is the political party leading the military training of Christians in Iraq. Yonadam Kanna, a politician from the group, said: "This is a fight to take back and come back to our land.
"It's as though our roots of thousands of years have been pulled out of the ground."
Patriarch Louis Sako, the head of the Chaldean Catholic Church and one of the biggest in Iraq, says he disapproves of Christians arming themselves against Islamic State.