Also believed to be included is the case of Major Mathew Golsteyn, an Army Green Beret accused of killing an unarmed Afghan in 2010, the Times said.
Reuters could not immediately identify a way to contact Gallagher and Golsteyn.
The newspaper reported that the cases of other men are believed to be included in the paperwork, without naming them.
The White House and the department of justice did not immediately respond to requests for comment about the report.
Legal experts cited in the report said that pardoning several accused and convicted war criminals, including some who have not yet gone to trial, has not been done in recent history, and some worried such pardons could erode the legitimacy of military law.