Black Cats chief Steve Bruce, Blues had last week sought permission to speak with Sbragia about replacing Roy Aitken, who quit the role to team up with David O'Leary at United Arab Emirates outfit Al Ahli.
However, Sbragia, a former Blues defender, has decided against a move to St Andrews in preference to remaining in his role as chief scout at The Stadium of Light.
"I'm delighted Ricky's staying with us," Bruce told the Sunderland Echo.
"He's done an excellent job for us on the scouting side, but coaching was his first love and he wanted to hear what Birmingham had to offer.
"He's spoken to Alex [McLeish], thought about it carefully and decided to stay at Sunderland, and we're very happy about that."