Dear Kantha,
To answer your query, yes the employee can be issued with show cause notice. However, we also need additional information.
What was the "misbehaviour"? Is there any code of conduct or rule in company manual that says fellow employee's personal matters should not be discussed? If yes, then do you have proof for that employee having "read and understood" the contents of this manual?
Has it happened with that female employee for the first time or has it happened earlier also?
Is this isolated case or in general personal matters are discussed in office and now all of a sudden you wanted to take action? Was it routine for that female employee to discuss her personal matters but this time she has raised red flag?
Please give due importance to all the above questions. Before issue of show cause notice, call the employee and try obtaining his consent on his wrongdoing. If he agrees then tell him to put up apology letter. This will avoid issue of show cause notice. On the strength of his apology letter, you may issue warning letter directly.
Yes, that employee might have erred, but then we are also responsible for his motivation level. If the matter is not handled properly it could impact his motivation and that is the last thing we can ask for.
Lastly, you may issue office circular stating that personal matters are not to be discussed or referred in the office.
Thanks,
Dinesh V Divekar