I'm extending a hand of friendship to you. But it's a bit formal. Most Americans wouldn't say that. A more casual version would be, "I'd like to be your friend." But still, it would only be used under certain conditions. When you meet a person for the first time, you merely greet them, and say, "I'm glad to meet you." Or, "It's nice to meet you." And then, you might hope you'll become friends, but few people would actually SAY that you want to be their friend.

I wouldn't use it if l'd just met someone and I wanted them to be my friend

Or you could say. I'm extending the hand of friendship to you

It's perfect