The Arizona Republic reported Sunday the mayor sent his request to the Justice Department this month. The department has not commented other than to say it would consider the request.
Gordon was concerned, the Republic said, about a "pattern and practice of conduct that includes discriminatory harassment, improper stops, searches and arrests."
The alleged pattern is based on a concerted effort by deputies to detain suspected illegal immigrants during traffic stops.
Arpaio told the newspaper the operation had the blessing of federal immigration officials, and he labeled Gordon's actions political.