The latter revealed in an essay for The Players’ Tribune that she is expecting their first child, a baby girl.
“Pregnant with our first child, Derek and I are looking to the future,” wrote Hannah, 26.
Weeks after she found out she was pregnant, Hannah posed for her fifth Sports Illustrated Swimsuit appearance, wearing an itty bitty bikini while photographed on the beach in Mexico.
The couple tied the knot in July of last year at Meadowood Napa Valley Resort in St. Helena, California. Hannah wore two couture gowns by Vera Wang as they exchanged vows in front of family and friends.
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In The Players’ Tribune 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. “Whatever her name is, I know she’ll run circles around him.”
RELATED VIDEO: Hannah Davis Ties the Knot With Yankee legend Derek Jeter
Despite their daughter — and any future children — being born into a “extraordinary situation,” the mom-to-be insists she wants them to see Derek as their father first and foremost.
“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,’ ” she writes. “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.”
Hannah hints that she’s due in May, writing, “I already can’t wait to show them footage of that last night at the Stadium. But I know it won’t be quite the same. I’ll tell them myself: You had to be there. And I’m sure that both of us will be thinking about that in May.”
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!”