The paper cited unnamed "people familiar with the matter." News Corp. did not respond to a request for comment Saturday.
Thomson is also editor in chief of Dow Jones, the News Corp. division that includes the Journal and a financial news service.
News Corp. said this summer that it will split into two public companies, one for its newspaper and book publishing business and the other for its fast-growing movie and TV operations. Rupert Murdoch, whose family controls the New York-based conglomerate, will be chairman of both companies.