The Haaretz newspaper said that a committee on senior civil service appointments has asked the JP Morgan Chase International chairman to explain why he failed to inform it of a 2006 incident in a duty-free shop at Hong Kong international airport.
"As he was leaving the store, a bottle of cologne that appeared not to have been paid for was found among Frenkel's belongings," the paper reported.
"A security guard then apprehended Frenkel and prevented him from boarding his flight, with the event captured on security cameras," it said.
He denies wrongdoing.
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"Local authorities in Hong Kong reached the conclusion that this was an unfortunate misunderstanding, and expressed their apology and their appreciation that I did not sue them for compensation," he said in a statement published in newspapers today.
"I expect to take office as governor of the Bank of Israel in early October," he added.
Israeli army radio said that the appointments committee would discuss his case later today.
Frenkel, 70, was named last month to replace former World Bank chief economist Stanley Fischer, 69, who is stepping down from the central bank governorship after eight years on the job.
Frenkel already held the post from 1991 to 2000.