Trump has repeatedly asked associates about bringing back execution by firing squad, hanging or guillotine, the report said, citing three people familiar with the matter.
Moreover, Trump has floated the idea of group executions and also mused about broadcasting executions, the report said.
Trump believes that such a policy would help "put the fear of God" into criminals, the report quoted one source as saying.
A Trump spokesperson denied that the former president considered a video advertisement campaign featuring moments from executions, calling the rumors "fake news from idiots," the report said.
During his 2024 presidential campaign announcement in November, Trump said he would urge the death penalty for drug dealers. Trump has argued that drug lords continue to operate behind bars and consequently must be executed instead of jailed, the report said, citing a former Trump White House official.
There are currently 44 men on federal death row in the United States, the report added.