The couple had already settled on a name months before Bündchen, 29, gave birth to a boy last Tuesday, but then she had a change of heart.
"It's kind of back to the drawing board," Brady, 32, said in an interview on WEEI Sports Radio. "We thought we had a name picked out for about six months and then about two days before he was born she said, 'I don't like that name anymore.'"
And Brady, who quickly returned to work as quarterback of the New England Patriots, says the couple will need more than the little time they can currently scrape together to have a serious discussion about the matter.
"She makes all these decisions," Brady joked, adding, "I haven't been home all week. We have about seven or eight choices. I have got to be home for more than just two-three hours so we can talk about it."
His only condition? "It will probably be a traditional [name]," he says. And though he doesn't mind choosing a Brazilian name, in honor of his wife's heritage, "I certainly want a name that I can pronounce!"