The group has no historic links with Burma, but owns ad agency Bates Myanmar, a subsidiary of Cordiant Communications, which WPP finally bought last month.
Bates Myanmar works for foreign investors, including British American Tobacco, a long-standing target of the Burma Campaign.
WPP's inclusion on the dirty list would have left it vulnerable to the charity's aggressive media offensive but PRWeek understands Sir Martin is poised to sever WPP's link with Bates Myanmar or withdraw the company.
A spokesperson said WPP is looking at its link to Bates Myanmar "with a great sense of urgency", adding that it is "close to closing" the firm.
The campaign's media officer Mark Farmaner said: "We are asking people to write, fax, email and call Sir Martin Sorrell, urging him to pull out of Burma.
"We will also target WPP investors, calling on them to abide by the CSR work of the company and demand WPP pulls out."
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