A wide range of cellular processes initiates upon recognizing and binding of proteins to specific DNA sites. Typically, the recognition process is incredibly fast owing to a complex mechanism that combines different 3D and ID modes of translocation of the protein. While few studies performed on selected DNA topologies suggested that the DNA topology might alter the balance between these two modes and therefore the target search kinetics, its detailed role in the target search mechanism remains unclear. Here, we present a discrete-state stochastic approach that allows us to incorporate the topological information of DNA molecule explicitly and predict its role during the process when proteins search for their specific binding sites on DNA. Applying the theory to the closed loop and different supercoiled DNA topologies, we find that the target search efficiency of the protein is strongly influenced by the DNA topology. Furthermore, if the topology is such that it promotes juxtaposition of distant DNA sites, the number, position and relative distances between such juxtaposition sites play a crucial role in facilitating the search process by providing additional routes to approach the target site. Our predictions are validated through extensive Monte Carlo simulations.