"Jeg har lyst til å bli venn med deg" OR "Jeg vil bli din venn"

Mat´s answer is correct, but I´ll add this: Norwegian people are introvert and non-direct by nature, and this is reflected in the language. It´s more common for them to ask of other peoples wishes or intents, rather than revealing their own. Following that logic, it would be more natural to say "Would you like to be my friend?" than "I would like to be your friend". In norwegian: "Vil du være vennen min?" or "Vil du bli venn med meg?"