I've tried to find anything that proves that the Org leader is someone close to Conan, but I have not learned anything useful (from searching only the main manga), so if anyone can brief me on this idea, it would be appreciated.

Necroed to preserve some OC that the forum changeover truncated.Solera wrote:It's because of this XD
Mysteries and Secrets Revealed! Volume 19: The Case Closed Casebook wrote:
Absolutely nothing is known about the person who commands the Black Organization and its members. It may be a man or woman, young or old, Asian or Westerner—not a single detail has come to light yet. Even Gin and Vermouth, senior syndicate members, refer to the leader only as “that person”.
The only hint given so far is the leader’s email address. Known only to a select few within the Black Organization, such as Vermouth, the email address plays a famous Japanese melody called “Nanatsu no Ko,” or “The Seventh Child.” According to Aoyama, the author, the name of “that person” has already appeared in the manga in some form.
It logically follows that the leader is someone readers are familiar with, so this hint has led to frantic fan speculation. Fan sites are abuzz with comments such as “Maybe it’s Professor Agasa!” or “It has to be Kogoro Mori!” Some theories are well-founded and compelling, while others are clearly crackpot suggestions meant only as jokes. However, any of them could still be true, until the author reveals the secret. The only other hint Aoyama has given so far is that “It’s someone that Haibara would never have expected.”
Aoyama also suggests that the true name of the syndicate, which has also never been revealed, is tied to the identity of its leader. If the Black Organization’s real name were revealed, everyone would know who its leader is. This may turn out to be the biggest hint of all.
Whatever the secret is, once it’s revealed, the Case Closed story will begin its final chapters. As a result, it may be some time before we find out who the mysterious leader really is…giving us all plenty of time to keep speculating.