This paper tackles the problem of nonprehensile object transportation through a legged manipulator. A whole-body control architecture is devised to prevent sliding of the object placed on the tray at the manipulator's end-effector and retain the legged robot balance during walking. The controller solves a quadratic optimization problem to realize the sought transportation task while maintaining the contact forces between the tray and the object and between the legs and the ground within their respective friction cones, also considering limits on the input torques. An extensive simulation campaign confirmed the feasibility of the approach and evaluated the control performance through a thorough statistical analysis conducted varying mass, friction, and the dimension of the transported object.