British police said on Friday they had interviewed two men under caution in relation to offences under a law covering abuses linked to the granting of honours.
In February, London's Metropolitan Police said they had begun an investigation into allegations in media reports that honours were offered to a Saudi national in return for donations to one of then-Prince Charles's charities.
Charles became king earlier this month following the death of his mother Queen Elizabeth.
"On Tuesday, 6 September, police interviewed a man aged in his 50s and a man aged in his 40s under caution in relation to offences under the Honours (Prevention of Abuses) Act 1925," the Metropolitan Police said in a statement on Friday.
"The investigation remains ongoing and we will not be providing a running commentary on its progress."
The Sunday Times newspaper reported last year that a Saudi businessman had received an award after paying thousands of pounds towards projects strongly supported by Charles, with the assistance of the then heir to the throne's aides.
Buckingham Palace did not immediately respond to a request for comment on the police statement.
A spokesperson for Charles has previously said the now-king had no knowledge of the alleged offer of honours or citizenship on the basis of donations.
Weeks after the newspaper report, Michael Fawcett, right-hand man to Charles for decades, stepped down from his role running the royal's charity, The Prince's Foundation.
(Reporting by Kylie MacLellan; Editing by Mark Potter)
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