Currently SMF already comes with a built-in 'Buddies List' but it's more of a personal list as it does not send a request of any form.
http://www.infinity-css.com/index.php?action=profile;area=listsAs per more 'Social Networking' that might be a possibility but that would probably require more than just the single feature your pointing out as I don't believe there is a mod out there that just integrates a 'Friends List', most of them are multi-features where it changes the whole profile and such, for example
Ultimate Profile.
EDIT: Installed on my forum just to get a quick preview since the mod's site is down.
https://imgur.com/A263Ajg,ZIVAHBB,X9sSbkoThe friend requests are sent via a 'Notifier' to your PM Box.
Also have your profile set to 'Ultimate' is optional.