Nuclei provide plenty of information about the micro-environment. An automatic nuclei segmentation approach can reduce the effort of pathologists and provide precise microenvironment observations for clinical investigations. Even though the current deep-learning (DL) based nuclei segmentation approaches perform better than the traditional ones in most cases, this task is still difficult, especially when the nuclei are cohesive and overlapping with each other. In this present work, we have suggested a novel nuclei segmentation method, where we combine the convolution neural network (CNN) based U-Net model with a Nonlocal Means (NLM) filter for pre-processing the source image. The NLM filter can eliminate the noise from the input image while retaining the edge details. The pre-processing step employed improves the effectiveness of the suggested segmentation method. The efficacy of the suggested method for segmenting nuclei is compared with the existing methods on the same dataset. The proposed method attained IOU(JI), Accuracy, Precision, and F1 score values as 0.8055, 96.29%, 0.8819, and 0.8944 respectively. The empirical results show that our proposed method performs better than the other existing techniques.