Discussions about whether to strike the American in Pakistan have been going on since the middle of last year.
The identity of the American citizen as well as other details about what he is accused of doing and the evidence against him of plotting attacks against Americans are not clear.
The report in the New York Times said it is also not clear how much "reluctance by the administration to approve a strike is based on whether he meets the standard - a continuing, imminent threat against Americans - and how much other factors, like the complications raised by the military preference, are playing a role."
Previously, the Obama administration had carried out a targeted killing operation against an American citizen in September 2011, when a CIA drone strike had killed radical preacher Anwar al-Awlaki in Yemen.
The White House acknowledged last year that four American citizens had been killed in drone strikes during Obama's tenure. Of these, only Awlaki had been intentionally targeted.
Offering a glimpse of the debate, Representative Mike Rogers of Michigan, chairman of the Intelligence Committee, spoke angrily about the drone restrictions imposed by President Barack Obama.
He said the new rules are "endangering the lives of Americans at home and our military overseas in a way that is frustrating to our allies and frustrating to those of us who engage in the oversight of our classified activities."
The administration's ambivalence on this case has infuriated Rogers.
"The chairman is fired up about this," a congressional aide said.
The aide also confirmed that the Defence Department was initially reluctant to place the American individual on the targeting list, questioning whether he met the new standards that Obama laid out last May.
