Clarke was expected to start in a role at DHS at the end of June, but according to one person close to the administration who is familiar with the situation, his appointment had been subject to significant delays that contributed to his withdrawal.
A spokesman for the Department of Homeland Security said: "Sheriff Clarke is no longer being considered for a position within DHS. We wish him well."
Trump and Clarke met in Wisconsin on Tuesday, according to Peterson, and they discussed other roles in which Clarke could support Trump.
"The sheriff is reviewing options inside and outside of government," Peterson said. "Sheriff Clarke told Secretary Kelly he is very appreciative of the tremendous opportunity the secretary was offering, and expressed his support for the secretary and the agency."
The Washington Post obtained a copy of the tentative job offer letter from the Department of Homeland Security offering Clarke the Assistant Secretary for Office of Partnership and Engagement/State and Local Law Enforcement position. The letter states that Clarke's position would be subject to final approval by the Office of Personnel Management.
The White House did not immediately respond to requests for comment.