In this manuscript, we give the definition of Riemannian concircular structure manifolds. Some basic properties and integrability condition of such manifolds are established. It is proved that a Riemannian concircular structure manifold is semisymmetric if and only if it is concircularly flat. We also prove that the Riemannian metric of a semisymmetric Riemannian concircular structure manifold is a generalized soliton. In this sequel, we show that a conformally flat Riemannian concircular structure manifold is a quasi-Einstein manifold and its scalar curvature satisfies the partial differential equation △r = ∂ 2 r ∂t 2 + α(n − 1) ∂r ∂t. To validate the existence of Riemannian concircular structure manifolds, we present some non-trivial examples. In this series, we show that a quasi-Einstein manifold with a divergence free concircular curvature tensor is a Riemannian concircular structure manifold.