My Daughter was just like that.
No biggie.
She is not, an insecure child at all.
BUT... among other people/groups, she was shy.
Even in Preschool.
So what.
Because... my daughter from young age, KNEW who she was. She is also not a follower. She is also very wise, about people and vibes and social situations. She... did not engage right away among people. She OBSERVED. Then, SHE would, by choice, engage or not or play with a child or not. SHE chose that. She used her own senses. She is very confident and outgoing, and at home. Just not so much outside.
But now at 8 years old, she is very much more social and less shy. Naturally.
We always just raised her, to be herself. And to know, herself. Which she does. Much more so that other kids her own age. I am proud of her.
She is not a follower and is very wise. Socially. And very mature for her age.
We never raised her to think that something was wrong with her.
She is herself.
She is perfectly fine.
NOT all kids, have to be outgoing or gregarious.
It is a mistake, to think that 'shyness' is the same as being 'timid' or insecure. It is NOT.
It is 2 different things.
Being shy or 'cautious' is not a bad thing.
It is a positive thing.
My daughter, is as I said, VERY wise for her age and she can easily distinguish between nice and not nice, people. And she consciously CHOOSES her friends... not just getting sucked up into the other kids antics or noxious behavior. She knows herself. And can and will speak up, when need be. She is NO shrinking-violet. Even if shy. But less so as she has gotten older.
Which is a very, good thing.