You know, I think I might get in touch with his teacher before I did anything else. She sees him "in action" every day and would probably have some valuable insights into what's going on.
If your son has problems in general fitting in or making friends, I wouldn't hesitate to help him out a little bit by inviting others over to the house or on a outing or two. But at 6, kids are going to start picking their own friends, playing with others around the neighborhood, etc. So I would look into why he's having trouble with the whole friendship thing.
My oldest son was always very social. He's intelligent, creative, imaginative, talkative...and he had a hard time at this same age not turning other kids off on himself. I was confused too, until I started watching more closely. I took him to park, watched him with friends in the neighborhood, etc. and discovered a few things. He tended to talk too much, too fast, without "sharing" the conversation. He tended to direct more than he play "together" and he didn't seem to get the idea of personal space, often standing too close for the other person's comfort.
I wasn't sure what exactly to make of it, but I decided to bring it up to him (gently of course). We would practice these skills at home so that I had the chance to literally pre-teach him. With a little work, he got the hang of it and now, at 12, does much better.
I have no idea if any of this applies to your son, just thought I'd throw it out there for you to see if it rings any bells. Either way, I hope you find a way that works to help your son. Good luck, and good for you for being such a supportive mother for your son!