The pair, who have been dating from quite a some time, is allegedly wanting to have a family, reported OK! magazine.
"They want to marry and have a family. They're discussing it," a source said.
But the couple's busy schedules are not allowing them to get married as soon as possible.
"They're madly in love, but no moves have been made yet because their schedules have been crazy," the source added.
Stone, 25, and Garfield, 28, are reportedly staying together after dating each other for about a year.