Just as a warning. I have a high functioning ASD daughter who had parallel play but would not join into the group. This can be a sign of high functioning autism spectrum. This is very unusual in girls and I have found many teachers in pre-school do not look for it. I saw the same signs and had to scream to get her noticed. The signs are not always obvious.

Luckily I did and she is doing much better now at 8. If the child does not engage socially by 4 at the latest this needs to be checked.

If your daughter doesn't become more social as she gets older, you may want to consider a Social Skills class led by a good therapist. I sent my 6-year old daughter to 8 social skills classes with a great therapist, and she learned how to approach and play with other kids through role playing and advice. It really helped her in a short period of time. She is much better at interacting and making friends now. I also help arrange a lot of playdates.
Hope this helps,
Elisabeth

My daughter is the same age and the same way. I've just reconciled with myself not to worry, it's her personality and not a developmental issue. I have similar traits myself, a balance of introverted/extroverted. She has the right social skills, knows how to greet people and often does spontaneously, initiates play and joins in on play. She has kids she clicks with very easily and those she just watches and never approaches and sometimes comments "he is noisy." As often as she plays with others, she plays independently or reads a book, which she loves to do. I think it's fine and a mark of a thoughtful personality. In order to be socially healthy we don't necessarily need to follow the group all the time and play with all kids all the time. Perhaps expectations for all young children to do this are a bit unrealistic?

My daughter was the same way. She actually went to 2 schools simultaneously - a daycare on my work days, and our town's public preschool on off days. The preschool teacher had an excellent way of handling this - she would allow our daughter 10 minutes at a solitary activity, and then take her by the hand and help her engage with other children in a group activity. I suggested this to the daycare teachers, and they employed this as well. Our daughter was never unhappy playing by herself - it just didn't occur to her to play with others. Once she was "helped" in doing so, she enjoyed group activities, too. Now, she is 5 years old and very social; though she still values some alone time now and then.

I wouldn't worry unless there are other worrisome signs. My son was like this at this age and now at 5 he's very social. 20 years ago your daughter would have been home with only you for company and you wouldn't be thinking about this at all.

My son didn't play with the other kids in his preschool class when he was three. I wasn't very concerned about it, since he was very social at the playground and in his playgroup and he was happy to go to preschool. I think being in a larger group of kids was off-putting. The teachers suggested scheduling playdates with one or two of the classmates he seemed to like so he could get to know them. I wish I had asked the teachers to encourage him to join the other kids, as one of the other commenters did. I think that's an idea worth trying.