Formal:
* ¿Quiere ser mi amigo/a? (Do you want to be my friend?) - This is the most formal way to say it.
* ¿Le gustaría ser mi amigo/a? (Would you like to be my friend?) - This is also formal and polite.
Informal:
* ¿Quieres ser mi amigo/a? (Do you want to be my friend?) - This is more casual and used with friends or people you know well.
* ¿Te gustaría ser mi amigo/a? (Would you like to be my friend?) - This is also casual and friendly.
Other options:
* Me gustaría que fueras mi amigo/a. (I would like you to be my friend.)
* Quiero que seas mi amigo/a. (I want you to be my friend.)
* Sería genial ser amigos. (It would be great to be friends.)
Remember to adjust the gender of the words "amigo" and "amiga" depending on the person you are talking to.