It was reported Girardi that had a six-hour meeting with the Yankees, including New York owner George Steinbrenner and his sons.
The Yankees also scheduled an interview with bench coach Don Mattingly on Tuesday, and made an appointment to visit with first base coach Tony Pena Wednesday. The New York Daily News reported that the team will conduct more interviews, though the names and number of candidates is not determined.
Girardi and Pena have both won Manager of the Year awards. Girardi won last season with the Florida Marlins, and Pena won in 2003 with the Kansas City Royals.
The Yankees are not expected to decide who will replace Torre until after the World Series. Torre turned down a one-year offer to return to the Yankees whom he directed to four World Series titles in 12 years.