Zhou said Lagarde had the bank's "quite full support," for the job, The Wall Street Journal reported Monday.
Backing from China could be the deal-maker, as Lagarde is considered the front-runner for the job that was left open when former Director Dominique Strauss-Kahn resigned to focus on fighting sexual assault charges in New York.
Zhou was in London along with a national entourage headed by Chinese Premier Wen Jiabao when he publicly endorsed Lagarde.
The other candidate for the job, Mexican central bank chief Agustin Carstens, has support from Canada and Australia. The United States has not stated a choice, the Journal said.
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