An iPad or an iPad mini were two of the suggestions, according to The Associated Press.
The first lady wasn’t giving away any secrets, explaining that the reporters present would spill the beans, but she promised "it will be something nice."
The first lady brought the family dog, Bo, along for the visit. He sat on her lap while she read "A Visit from St. Nicholas" to about 200 patients.
It is a tradition dating back to former President Truman's wife Bess for the first lady to visit the Washington hospital during the holiday season, according to the White House. The annual Christmas in Washington charity concert, which the president and first lady attended last weekend, also benefits Children's National Medical Center.
Michelle Obama's visit was scheduled to take place shortly after President Obama addressed the shooting at an elementary school in Connecticut, but she did not address the violence.