Leeks, of Frederick, Md., said he asked for the date while the two were sorting Christmas gifts for needy children at Toys for Tots in Washington.
"She said, 'yes.' She'd love to go with me," he said.
Leeks is awaiting confirmation from the White House that the first lady will, indeed, be his date to the November 2012 ball, ABC News reported Sunday.
"The reason she's checking with her husband is to make sure that week is clear," Leeks said.
Within 45 days, Leeks will be heading to Afghanistan, where he is assigned to mortuary affairs.
"We process remains from fallen soldiers," Leeks said. "We're the last line from the fallen soldier to their family. Our job is to bring them back. Not too many people can do this."
The marine acknowledged that asking the first lady to the ball was a bold thing to do.
"A few people asked me, 'Did you just ask your boss' boss' boss' wife out?'" Leeks said.
Leeks, whose fiancee, also a marine, is stationed in Okinawa, Japan, said his request is a "thank you" for Michelle Obama's outreach and support of military families.
"I knew how supportive the first lady is of the family structure, in general, and especially military families," he said.