In a statement to CNBC, Kushner's lawyer, Abbe Lowell, also said that his client sat "for two interviews with the Office of Special Counsel."
The second interview lasted for more than six hours, and included questions regarding the Trump campaign and the transition period before the presidential inauguration, as well as the Comey firing, NBC reported, citing a source familiar with the interview.
Kushner, a senior White House advisor, had reportedly met with special counsel Robert Mueller's team for the first time in November as part of the probe of potential links between Trump's presidential campaign and Russia.
Career officials approved Kushner's permanent security clearance after the completion of an FBI background check process. The president was reportedly not involved in that process.
Several White House officials with interim security clearances had been downgraded in February, chief of staff John Kelly wrote in a memo at the time.
Lowell told CNBC on Wednesday that his client's application "was properly submitted, reviewed by numerous career officials and underwent the normal process."
He added: "Having completed all of these processes, he's looking forward to continuing to do the work the president has asked him to do."
Neither the special counsel nor the White House immediately responded to CNBC's requests for comment.