Washington (CNN) Less than 48 hours before the acting Homeland Security secretary is set to leave his post, President Donald Trump has yet to pick a successor despite promising to do so two weeks ago.

Trump administration officials have scrambled in recent days to find a legal workaround that would keep two immigration hardliners Trump favors for the job in contention, even after White House officials concluded they were ineligible. But with acting Homeland Security Secretary Kevin McAleenan's Thursday departure date rapidly approaching, officials said McAleenan could stay up to a week longer to ensure a smooth transition.

McAleenan indicated Wednesday that he is open to the possibility of staying on until a successor is named.

"I hope a plan for the successor is imminent, but if necessary, I will absolutely ensure a smooth transition," he said during a House Homeland Security Committee hearing, where he was testifying on global terror threats.

Just last week, White House officials determined that nether Ken Cuccinelli, the acting director of Citizenship and Immigration Services, nor Mark Morgan, the acting Customs and Border Protection chief, were eligible to succeed McAleenan as acting secretary because they had not served at least 90 days under the last Senate-confirmed Homeland Security secretary, Kirstjen Nielsen, who left office in April.

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