Mazzone, who has been on Atlanta's staff with manager Bobby Cox since June 1990, is considered one of the top pitching coaches in the Major Leagues, helping the Braves win 14 consecutive division titles.
A source confirmed that the Yankees had asked for and received permission to speak with Mazzone, though it is unclear when the two sides will speak. Mazzone has one year remaining on his contract with the Braves.
Yankees general manager Brian Cashman, whose future is uncertain as his contract expires on Oct. 31, did not return calls.
Stottlemyre announced last week that he would not return for an 11th season on Joe Torre's staff, saying he was tired of the constant criticism and the division between the New York and Tampa factions in the organization.
Torre's future remains a bit of a mystery as well. The manager has yet to address the media following New York's American League Division Series loss to the Angels, though he is expected to do so sometime this week.
Mazzone, who turned 57 on Sunday, had a positive impact on Jaret Wright during the pitcher's year-and-a-half stint in Atlanta. Wright endorsed the idea of Mazzone taking over for Stottlemyre last week.
"He helped me out a lot, and he's done that for a lot of years with a lot of guys," Wright said. "He's a professional. I think he could do a good job."
Other possible candidates include former Yankees left-hander Ron Guidry, Triple-A Columbus pitching coach Gil Patterson, Giants pitching coach Dave Righetti and former Red Sox pitching coach and current Yankees advance scout Joe Kerrigan.
Mark Feinsand is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.