President Trump is expected to nominate former Virginia attorney general Kenneth Cuccinelli to oversee the nation's immigration system as the next director of the U.S. Citizenship and Immigration Services, according to media reports.

Cuccinelli -- an immigration hardliner -- would replace Lee Francis Cissna, who is resigning after pressure from the White House, the New York Times reported. He officially steps down June 1. Trump has long-regarded the country's immigration system as broken and in need of restructuring.

Cissna had support from a number of groups opposed to illegal immigration, but not from White House officials.

While Cuccinelli has Trump's support, getting confirmed to the post could be a problem. The Times reports that Senate Majority Leader Mitch McConnell said his chances were close to zero.

Cuccinelli in 2014 was part of the Senate Conservatives Fund political action committee that supported Kentucky Gov. Matt Bevin to challenge McConnell in a primary, according to the paper.

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McConnell previously said he opposed Cuccinelli to head the Department of Homeland Security after Kirstjen Nielsen was fired last month.

"I've not spoken to him about any of them. I have expressed my, shall I say, lack of enthusiasm for one of them … Ken Cuccinelli," McConnell told reporters in April.