This paper is aimed at developing optimal motion planning for a single autonomous surface vehicle (ASV) equipped with an on-board pollutant sensor that will maximize the sensor-related information available for source seeking. The ASV uses a nonlinear diffusion model of the pollutant source to estimate the intensity/level of the pollution at the present ASV location. The rate of detection of particles depends on the relative distance between the ASV and the source. First, we use a probabilistic map of the source location built through the sensor information for a dynamic motion planning of source seeking based on an entropy reduction formulation, where an appropriately defined Fisher information matrix (FIM) is used for entropy reduction or information gain. We derive the FIM for the set-up and investigate optimal trajectories. Next, we present an online nonlinear Monte Carlo algorithm that uses the obtained sensor information about pollutant at different vehicle locations to update a probabilistic uncertainty map of pollutant source location. As the mission unfolds the ASV motion is computed by considering a moving-horizon interval of decision, which will allow for the inclusion of new information available for optimal motion planning. The proposed motion planning approach is extended to take into account external disturbances and it is able to minimize the uncertainty in the pollutant source. Finally, we provide two case studies to demonstrate efficacy of the proposed motion planning algorithm.