But the governor will be rooting from the stands for Stanford when the Cardinal play Michigan State in the Rose Bowl on New Year's Day.
Brown will be joined by his wife, Anne Gust Brown, who graduated from Stanford and went to law school at University of Michigan, a Michigan State rival.
The governor's office said Brown and Gust Brown bought their own tickets to the game. They will not participate in the Rose Parade.
Any wager Brown might make with Michigan Gov. Rick Snyder appeared to be unsettled, but the tough talk is already on.
"We'll let you know if there's a wager," Brown spokesman Evan Westrup said in an email, "but based on recent history, our friends from the Big 10 have a big hill to climb if they hope to beat the Cardinal."
No. 5 Stanford is ranked just behind No. 4 Michigan State, but Westrup had recent Rose Bowl history in mind. Big Ten teams have lost eight of nine Rose Bowl games in the last decade.
Editor's note: This post was updated at 3:45 p.m. to include information about team rankings and the Big Ten's struggles in recent Rose Bowl games.
PHOTO: Stanford quarterback Kevin Hogan celebrates after a college football game on Thursday, Nov. 7, 2013, in Stanford, Calif. AP Photo/Marcio Jose Sanchez