In the current NISQ era, it has become difficult to schedule increasingly complex quantum tasks with limited connectivity of the QPU (Quantum Processing Unit). This is partially attributed to the fact that we require qubits that share a task to be physically connected in the hardware topology. To satisfy this connectivity constraint, quantum circuits must make use of SWAP gates or reversing existing CNOT gates. Adding these gates comes with added computational cost and errors, which creates a need for efficient routing agents that can optimize this problem of qubit routing. We present a Nested Monte Carlo Search (NMCS) based agent (NesQ router) which aims to solve this problem by efficiently sampling the state space. In our experiments, NesQ was able to outperform other routing algorithms while offering a much lower runtime.