support for making friends

I would like to support my ten year old daughter in making friendships - any ideas?

She often has one or two very good friends who she goes around with at school but it never progresses to more than that in the way I know she would like. What I see is that this is mostly because she does not make any more advances or seem that interested.

She has recently started at a new secondary school. She speaks about her 'friends' at school and there are two girls she likes.

Now we often go swimming at the local pool on Saturday (me, my younger child and my older ten year old) and I suggested she tell one of her friends this and we could meet her there.

I made this suggestion because my daughter already told me that this girls likes swimming.

My daughter is very reluctant to ask. Though I can see she would like to.

Was my suggestion off key? Should I push it a bit? If I leave it I know the friendship won't progress beyond the basics. It's happened before. I see she wants to see this girl outside of school but is scared. Can I do anything else to help??