WASHINGTON—The House Judiciary Committee is eyeing additional document requests to associates of President Trump, including Trump lawyer Rudy Giuliani and a former lawyer for Michael Cohen who last year sought a pardon on his client’s behalf, according to a person familiar with the committee’s plans.

Other individuals likely to be sent requests include former Secretary of State Rex Tillerson and Gary Cohn, an investment banker who served as Mr. Trump’s top economic adviser until he stepped down one year ago.

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