If its someone you met on the street randomly, I wouldn't recommend having any conversation.
If it's someone you met through some activity, and they aren't a random person from the streets, it's a more convenient opportunity for friendship.
But you never explicitly "ask" to be friends with anybody, it just happens. Friendship comes by itself, it doesn't have to be a formal thing, or a declaration of "I am your friend".
I know many people who I know are my friends, but we never actually told each other or asked each other, we both already realize we are friends.