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Mr. Obama’s Tuesday press conference is scheduled for Dodge Renaissance Academy on the West Side of Chicago. Mr. Duncan has led Chicago’s schools since 2001.

The Obama transition team would not comment on whether Mr. Duncan would be nominated.

Whitney Tilson, a prominent New York fundraiser for Mr. Obama who was a founder of Democrats for Education Reform, told The Washington Times that Mr. Duncan inherited one of the worst school systems in the nation, and its third largest, and turned it around as a genuine reformer.

Ben Conery, Jennifer Haberkorn and Tom LoBianco contributed to this article.