Hannah, 26, revealed in an essay for The Players’ Tribune that she is pregnant with their first child, a baby girl.
The couple wed in July.
In the piece, which include a photo of Derek holding a bouquet of pink balloons, the model revealed that the New York Yankees legend, 42, already has a name picked out for their baby — however, she’s not set on it just yet.
“He’ll say when he calls me during the day: ‘So, how are you and so-and-so doing?’ ” she writes.
“‘That’s not the name yet, sweetie,’ ” Hannah reminds him.
She writes, “Whatever her name is, I know she’ll run circles around him.”
“We want our kids’ lives to be as ‘normal’ as possible,” she continues. “They’re going to be born into such an extraordinary situation. They’re going to have to be some strong little people. We don’t want them to be defined by their dad’s name — for them, we want him to just be ‘Dad.’ That will be the piece of him they’ll have that the rest of the world doesn’t. It will be special, and it will be theirs.”
In December 2014, Derek said he was looking forward to fatherhood, but admitted he was happy with being an uncle until then.
“I look forward to being a dad,” he told PEOPLE, joking, “When you’re an uncle, you can get rid of them when you want to get rid of them!”