Kelly issued the memo after the White House faced criticism that Rob Porter, who resigned amid domestic abuse accusations, handled classified information on a temporary clearance despite an Federal Bureau of Investigation background check that triggered concerns.
Kushner's close relationship to the president has given him access to highly classified information despite his own interim clearance, and he is able to read Trump's daily presidential brief.
Late Tuesday, the New York Times reported that Kushner and Kelly clashed over the security clearance and that Kushner believed that Kelly had targeted him personally.
Kelly, in a statement, said the White House looks forward to Kushner maintaining his role working on the Middle East peace process and U.S. -Mexico relations. Sanders did not rule out President Donald Trump using his executive authority to grant Kushner a permanent security clearance, which would circumvent the traditional process run by the White House office of personnel security.
The New York Times reported earlier on Tuesday that Kelly and Kushner had gotten into a dispute over the issue of Kushner's access to sensitive, classified intelligence. But Mr. Kelly, who has been privately dismissive of Mr. Kushner since taking the post of chief of staff but has rarely taken him on directly, has made no guarantees.
The reason for this attempt by Kelly, according to the report, is the scandal involving former White House aide Rob Porter, who has been accused of domestic violence. Kelly has interpreted that as a wide-ranging mandate that would include Kushner, a person familiar with the matter said.
The fallout from that is what's prompting the overhaul, which Kelly signed off on last week.
Kelly also coached White House press secretary Sarah Sanders on how to answer when asked about Kushner's clearance issues.
"Everyone in the White House is grateful for these valuable contributions to furthering the President's agenda".
"First of all, I'm not aware of any red flags, and I think it's irresponsible to suggest that without having seen any individual's file", she said. "And he'll continue to do the important work that he's been focused on with the a year ago".