The Post said a Democratic official familiar with the situation had revealed Obama would introduce the former Army chief of staff as his choice for the Cabinet-level post Sunday.
The Post also reported that Obama said in an exclusive interview with NBC News, to be aired on "Meet the Press," that Shinseki is "exactly the right person who is going to be able to make sure that we honor our troops when they come home."
Shinseki's national profile zoomed up nearly six years ago when he told the Senate Armed Services Committee that "something on the order of several hundred thousand soldiers" could be necessary to win the war in Iraq. Then-Defense Secretary Donald Rumsfeld said Shinseki's estimate "will prove to be high."
Three years later, Gen. John Abizaid, commander of U.S. Central Command, told the same Senate panel, Shinseki was right.
Shinseki retired in the summer of 2003 and has since joined the boards of Honeywell International Inc. and Ducommun Inc., both companies focused on military contracting. He also is on the board of the Hawaiian companies Grove Farm Corp. and First Hawaiian Bank.