The book, "Kill or Capture: The War on Terror and the Soul of the Obama Presidency," by Daniel Klaidman says Holder also was depressed about his mother's death and increasing criticism in the media, The Washington Post reported.
Resigning "will not be good for you and it will not be good for your friend, the president," Jarrett told Holder in a scene described by Klaidman, a Newsweek special correspondent and the magazine's former managing editor.
Holder, through a spokeswoman, declined to comment. The White House also declined to comment, the Post said.
Holder's relationship with the White House has improved dramatically since the departure of former Chief of Staff Rahm Emanuel, now mayor of Chicago, and David Axelrod, now an Obama campaign strategist, current and former Justice Department officials said.
"Now, Eric Holder is very comfortable wearing the mantle of attorney general, because he feels he has allies within the White House and not the detractors he had before," a former Justice Department official said.
Holder has faced Republican criticism related to the failed Fast and Furious gun-tracking program.