The US State Department is investigating the apparent disappearance of a bottle of whisky worth nearly $6,000 (£4,320).
The Japanese government gave the bottle to Mr Pompeo in June 2019 when the then-secretary of state visited the country.
The department reported the investigation in its annual accounting of gifts given to senior US officials by foreign governments and leaders.
It noted that it could find no trace of the bottle’s whereabouts and that there was an “ongoing inquiry” seeking an explanation.
A spokesman for Mr Pompeo said he was unaware of the gift and the inquiry into its whereabouts.
It is thought the bottle of whisky was given to Mr Pompeo while he was attending a G20 summit in Japan, along with then-president Donald Trump.
But the state department’s Office of Protocol, which records gifts given to US officials, said that, while every other gift had been recorded, there was no record of the whisky.
If a gift is over a certain value, the recipient can give it to the National Archives or another government entity, or they can keep the gift and reimburse the Treasury Department.
Among the items given to Mr Pompeo during his time as secretary of state were two carpets worth a total of $19,400 (£14,000) from the president of Kazakhstan and the foreign minister of the United Arab Emirates.
Mr Trump and his wife Melania received more than $120,000 (£86,400) worth of presents from foreign leaders in 2019, including an Ottoman Empire rifle worth $8,500 (£6,120) from the Bulgarian prime minister, a bronze sculpture of an Arabian horse from the crown prince of Bahrain worth $7,200 (£5,100), and a statue of an Arabian oryx worth $6,300 (£4,500) from the emir of Qatar.
The Office of Protocol said all of these were given to the National Archives.