Personally I think you shouldn’t worry about fans at all and concentrate on getting more friends. You can even send friend invitations to your fans. Not everyone knows that you can be a friend and a fan of an author. I would include a note that you are sending the invitation because you saw their name on your list of fans.
Goodreads does have a friend finder function on the friends page so you can find or invite friends from Gmail, Facebook, Hotmail, Twitter and Yahoo. It also lets you look through a list of friends of friends on Goodreads.
You should invite your twitter followers, facebook friends, facebook fans and blog readers to friend you on goodreads — don’t forget to provide a link.
Try friending authors you know and authors you read. Join groups, and not just groups for writers, you want to make connections with readers. Please don’t recommend your books to your friends or spam groups with messages about your books. Your friends, fans and followers can see your blog posts in their update feeds or by email, that’s the best place to promote your books.
Enter at least some of the books you have read, especially ones you enjoyed in the genres you write in. This will make it easier to compare books with potential friends. Add your own books to your shelves and create custom shelves for each genre your books belong in. To learn more about comparing books, read the post How does compare books work?