O'Neill has transformed the Black Cats' fortunes since replacing Steve Bruce at the Stadium of Light.
"At man-management he is the best there is, incredible," said ESPN football analyst Savage, who will be working with the broadcaster as part of their FA Cup third-round coverage this weekend.
"That is why Martin O'Neill is one of the best. Tactically he would not compare with Arsene Wenger but management is more than just picking a team.
"He knows players. He knew he could hammer me and I'd come out and want to prove him wrong. Other players would go into their shell if he did that."