Boone, who helped the Yankees to a 2003 World Series title with a walk-off home run in Game 7 of the American League Championship Series against the Boston Red Sox, interviewed recently with his former team.
The New York Daily News reported that the Yankees' brass likes Boone's "polish."
New York general manager Brian Cashman reportedly is intrigued by Boone despite no previous managerial or coaching experience. Boone has been serving as an analyst with ESPN.
Cashman recommended Boone to owner Hal Steinbrenner from a pool of six interviewees that included Carlos Beltran, Hensley Meulens, Rob Thomson, Chris Woodward and Eric Wedge. The search for Girardi's replacement took over a month.
Various media reports earlier Friday suggested that the decision came down to Boone and Meulens after Beltran and Thomson were both informed that they were not getting the job.
Meulens is currently working as the bench coach for the San Francisco Giants and was on the coaching staff for all three of the Giants' World Series championships in 2010, 2012 and 2014.
Meulens is a former top prospect in the Yankees organization who played parts of seven major league seasons from 1989 to 1998, including five with New York.