Wolf had authored a memo calling for the separation of families at the border. Cuccinelli is an immigration hard-liner who was once seen as President Trump's pick for the top job.
President Trump has told some Senate Republicans that he wants immigration hard-liner Ken Cuccinelli in charge of Homeland Security. But sources say he is concerned his party won't back the pick.
White House staffers have told President Trump he can't choose two immigration hard-liners for a top job because of federal vacancy rules, according to two people familiar with the conversations.