In this paper, starting from the common foundation of Connes' noncommutative geometry (NCG), various possible alternatives in the formulation of a theory of gravity in noncommutative spacetime are discussed in details. The diversity in the final physical content of the theory is shown to be the consequence of the arbitrary choices in each construction steps. As an alternative in the last step, when the structure equations are to be solved, a minimal set of constraints on the torsion and connection isfound to determine all the geometric notions in terms of the metric. In the Connes-Loft model of noncommutative spacetime, in order to keep the full spectrum of the discretized Kaluza-Klein theory, it is necessary to include the torsion in the generalized Einstein-Hilbert-Cartan action.