(CNN) White House officials Jared Kushner and John Kelly are privately feuding over Kushner's access to classified information despite having only an interim security clearance, according to a report in The New York Times.

The report said Kushner is concerned that Kelly, the chief of staff, had targeted him specifically with a recent directive to overhaul the White House clearance system.

Citing White House officials and others briefed on the matter, the Times reported Tuesday that Kushner is pushing back on giving up access to classified information. Kushner's security clearance has provided the senior White House adviser and son-in-law to President Donald Trump with highly classified information -- including the Presidential Daily Brief or "PDB" -- despite the fact that he lacks permanent clearance, according to the Times.

Nearly a year into the Trump administration, some senior-level staffers -- including daughter Ivanka Trump and her husband, Kushner -- remained on interim clearances even as other senior advisers were granted full security access, according to information obtained by CNN from a US government official

The White House security clearance process has been under scrutiny after former White House staff secretary Rob Porter was forced to resign when allegations of abuse from his previous spouses surfaced. Kelly, under fire over the White House's handling of the domestic abuse allegations against Porter, ordered an overhaul of the security clearance process for current and incoming top administration officials.

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