Barbour is a potential 2012 Republican presidential candidate.
Questioned by reporters Tuesday after an energy speech in Jackson, Barbour said he doesn't think Mississippi legislators will approve the Forrest license plate proposed by the Mississippi Division of Sons of Confederate Veterans.
The group wants to sponsor a series of state-issued license plates over the next few years to mark the 150th anniversary of the Civil War - or in its words, the "War Between the States." The Forrest license plate would be slated for 2014.
Mississippi NAACP president Derrick Johnson said it's "absurd" to honor a "racially divisive figure" such as Forrest. Johnson has also called on Barbour to denounce the license plate idea.
Asked about the NAACP's stance Tuesday, Barbour replied: "I don't go around denouncing people. That's not going to happen. I don't even denounce the news media."
Asked to clarify what he thinks is not going to happen, Barbour said he believes lawmakers won't approve a specialty license plate depicting Forrest.
"I know there's not a chance it'll become law," Barbour said.
Forrest, a Tennessee native, is revered by some as a military genius and reviled by others for leading an 1864 massacre of black Union troops at Fort Pillow, Tenn. Forrest was a Ku Klux Klan grand wizard in Tennessee after the war.
Johnson of the National Association for the Advancement of Colored People said Tuesday that Barbour's response to the proposed license plate was insufficient.
"I find it curious that the governor won't come out and clearly denounce the efforts of the Sons of Confederate Veterans to honor Nathan Bedford Forrest," Johnson said. "As the head of the state, he shouldn't tap dance around the question."
Sons of Confederate Veterans member Greg Stewart told The Associated Press last week he believes Forrest distanced himself from the Klan later in life. It's a point many historians agree upon, though some believe it was too little, too late, because the Klan had already turned violent before Forrest left.
"If Christian redemption means anything - and we all want redemption, I think - he redeemed himself in his own time, in his own actions, in his own words," Stewart said. "We should respect that."