Earlier this week, the team had second interviews with Rangers assistant general manager A.J. Preller and Red Sox assistant general manager Mike Hazen.
The team is going through its last round of interviews with four finalists before deciding on a successor for Josh Byrnes, who was dismissed on June 22.
Team executive chairman Ron Fowler and CEO and team president Mike Dee expect to have Kim Ng, the senior vice president of baseball operations for Major League Baseball, in for her second interview this week.
Fowler said recently that he hopes to have a general manager hired by early August.
Eppler is a San Diego native who went to University of San Diego High.
Eppler joined the Yankees in 2004, and he was their director of pro scouting (2005-11) before being promoted to assistant general manager.
The Yankees' media guide states that Eppler assists general manager Brian Cashman "in all areas of Major League Operations including player acquisitions, roster composition and management, staffing and personnel decisions, and player contract negotiations. In addition, he oversees all phases and personnel in the Yankees' Major League and professional scouting departments both domestically and internationally."
A total of eight candidates had initial interviews -- former Marlins general manager Larry Beinfest, Dodgers vice president of amateur scouting Logan White, D-backs scouting director Ray Montgomery, Eppler, Preller, Hazen, Padres assistant general manager Josh Stein and Ng.
Six candidates declined to be interviewed, the latest being current Padres assistant general manager A.J. Hinch, who is presiding over the day-to-day operations of the big league team.
Five others declined interviews: David Forst of the A's, Mike Chernoff of the Indians and Jason McLeod of the Cubs, Michael Girsch of the Cardinals and Padres senior vice president of baseball operations, Omar Minaya.
Forst, Chernoff and Girsch are assistant general managers. McLeod, who previously worked for the Padres, is the Cubs' scouting director.