WASHINGTON-—Former national security adviser Mike Flynn interacted with a graduate student with dual Russian and British nationalities at a 2014 U.K. security conference, a contact that came to the notice of U.S. intelligence but that Mr. Flynn, then the director of the Defense Intelligence Agency, didn’t disclose, according to people familiar with the matter.

Mr. Flynn met Svetlana Lokhova at the Cambridge Intelligence Seminar, a gathering of former intelligence officials hosted at Cambridge University, in February 2014. Ms. Lokhova at the time was a graduate student studying the history of Russian intelligence, according to two people who attended the event.

There is no record showing that Mr. Flynn reported his interaction with Ms. Lokhova to security officials in the Defense Department, said a former senior U.S. official with knowledge of the matter. As the director of the Defense Intelligence Agency, which is part of the Pentagon and the military’s largest intelligence organization, Mr. Flynn was expected to notify officials about any contacts with foreigners he didn’t know, particularly from an adversary nation such as Russia, the former official said.

The rules on “self-reporting” of such contacts aren’t iron-clad, but officials at Mr. Flynn’s level of security clearance are generally instructed to view approaches by foreign strangers as a possible attempt to gain sensitive information or even recruit a senior official on behalf of a foreign government.

“A senior official like him definitely ought to be expected to detect that and report it,” the former official said, adding that people who have worked in intelligence as long as Mr. Flynn are “indoctrinated to report any anomalous behavior that you detect.”