A new distinct cultivar of Osteospermum plant named ‘DAOSTREOGTYVE’, characterized by being a compact cultivar, with globular upright to spreading shape Very well branching (8-14 per plant) with stiff and strong lateral stems and small thick leaves. Color of leaves green RHS 139A (upper side) and green RHS 137B (underside) Ray florets being RHS Red 39A when opening and developing into RHS Red 53B when fully open on upper side and disc florets that appear RHS grayed-orange 166A.