There are variants for "I Wanna Be Friend of Yours" from college sources. The music is public domain. The lyrics were written by Kermit Goell. Copyrighted 19 Jan 1947.

This Kermit Goell's version was sung by Nat King Cole later in 1947. Will not post the copyrighted version.

I wanna be a friend of yours. w Kermit Goell , m : public domain . © 19Jan47 ; EU59856 . Kermit Goell.

See here: https://books.google.com/books?id=WE8hAQAAIAAJ&pg=PA2386&dq=%22friend+of+yours%22+%22kermit+goell%22&hl=en&newbks=1&newbks_redir=1&sa=X&ved=2ahUKEwju99X9iIP4AhU0TTABHcU-AdQQ6AF6BAgJEAI