"They are taking a break," an insider told the magazine. "It is because of busy schedules."
Anthony, 45, is divorced from singer-actress Jennifer Lopez, the mother of his 5-year-old twins.
Green, 22, is the British heiress to the Topshop fortune, UsMagazine.com said.
Celebrity Families of 2014 [PHOTOS]
Gwen Stefani finishing new solo album in Miami