The London institution revealed last week that the force is investigating items that are “missing, stolen or damaged” from its collection.
In a statement on Thursday to the PA news agency, police said: “A man has been interviewed by investigating officers. No arrests have been made.
“We have worked closely with the British Museum and will continue to do so.
“We will not be providing any further information at this time. Inquiries continue.”
An unnamed member of staff has been sacked and the London-based institution is taking legal action.
It is understood that the items, which include gold jewellery, gems of semi-precious stones and glass, were taken before 2023 and over a “significant” period of time.
Hundreds of historical artefacts have gone missing from the British Museum since 2013, the institution’s records reportedly show.
Gold coins, silver necklaces and 540 pieces of pottery are unaccounted for.
The Times reported on Thursday that an FOI request to the museum has disclosed that a Greek silver coin, a 4th-century Roman coin and a German coin disappeared from the museum in the year to April 2014.
An early 20th-century ring, a chain made up of “round-sectioned silver wire”, wooden opium poppy scorers shaped like birds and frogs, and glazed leaf pendants and beads are also said to be among the items missing over the last 10 years.
Art dealer Ittai Gradel contacted the museum in February 2021 after spotting items he had seen in its catalogues.
Director Hartwig Fischer told PA on Wednesday: “When allegations were brought to us in 2021 we took them incredibly seriously, and immediately set up an investigation.
“Concerns were only raised about a small number of items, and our investigation concluded that those items were all accounted for.
“We now have reason to believe that the individual who raised concerns had many more items in his possession, and it’s frustrating that that was not revealed to us as it would have aided our investigations.”
But Mr Gradel said any claim that he withheld information from the museum “is an outright lie”.
“I was explicit in my communication with the British Museum that I was entirely at their disposal for any further information or assistance they would require. They never contacted me,” he told PA.
In July, the museum announced that Mr Fischer, a German art historian, will step down from his role next year.
In the same month the museum sacked Peter Higgs, its curator of Mediterranean cultures, following an internal investigation into the disappearance of jewels made of gold, semi-precious stones and glass.
Reports have said the number of stolen artefacts from the British Museum is “closer to 2,000” with the total value of missing pieces thought to run into “millions of pounds”.
An independent review of security has been launched and the matter is also under investigation by the economic crime command of the Metropolitan Police.
The British Museum has been approached for comment.
The museum has not specified how many items have been stolen or detailed what the missing items are, saying only that they are “small pieces” dating from the “15th century BC to the 19th century AD”.