If you are good in Python/R there are couple of scripts available. If not, try ImageJ- depends on what depth of morphometry analysis you want to do. You can also use NucleusJ plugin in Image J. Check these paper-

https://academic.oup.com/bioinformatics/article/31/7/1144/181006

Article Objective assessment of changes in nuclear morphology and ce...

https://www.nature.com/articles/s41598-018-31924-2

Good Luck !!!

Depends on how much detail you need from the image as suggested by Prit Benny Malgulwar . You can also try CellProfiler (https://cellprofiler.org/) which comes with pipelines and their support is good. If the nucleus has to be classified based on features, you can try machine learning algorithms depending on what is available to you.

Good luck!

@Sathya

Thank you, Sathya Srinivasan and Prit Benny Malgulwar for your suggestions. I will try to use ImajeJ.