The world’s largest advertising agency has appointed independent counsel to look into the claim against the 73-year-old, who denies wrongdoing.
According to the Wall Street Journal, WPP’s board is looking into whether Sir Martin misused company funds.
In a statement, the company said: “The investigation is ongoing. The allegations do not involve amounts which are material to WPP.”
Sir Martin, who has been at the helm of WPP for more than three decades, has said he rejects the allegations “unreservedly”.
His statement added: “Reports in the media have stated that WPP is investigating an allegation of financial impropriety by me, specifically as to the use of company funds.
“I reject the allegation unreservedly but recognise that the company has to investigate it.
“I understand that this process will be completed shortly.
“Obviously, I shall play no part in the management of the investigation under way.”
There was no further detail given about the nature of the allegation. WPP’s shares were down 2.4% in early trading on Wednesday.
Sir Martin is one of the country’s best-known business leaders, having grown WPP from a two-man operation in 1985 to an advertising group that now dominates the industry with about 134,000 staff in more than 100 countries.
He previously worked at Saatchi & Saatchi and was knighted in the Queen’s 2000 New Year Honours list.
Sir Martin has been Britain’s highest-paid CEO for years, earning around £70m in 2015 before shareholders cut his pay to £48m the following year.