Should I talk to my boss about gossip.

I work in what I would call small salon, (it’s a small business but we have about 35 employees.

One of my co workers who i am pretty close with over heard the front desk girl talking about me and then when she walked up they started whispering. I really am conflicted because 1 I have only worked there for a little over half a year I don’t want to snitch on someone who has been there longer and is close with the boss 2 I try to avoid all the girls already out of fear that they will not like me 3 I struggle with depression and anxiety and knowing that they were gossiping about me loud enough for someone to over hear and possibly make their opinion about me based on what she says makes me feel really bad about myself.

This girl that said this is constantly gossiping, and overall doesn’t do her job well (but I don’t want to bring that into it)

How do I approach mentioning to my boss that it makes me uncomfortable without being a snitch ?

Or should I say nothing at all.