Cora, who currently serves as an ESPN analyst as well as general manager and manager of the Criollos de Caguas of the Puerto Rican winter baseball league, met with general manager A.J. Preller and other franchise executives Wednesday, the source said.
The 39-year-old Cora interviewed for the same role with the Texas Rangers last year.
Playing mostly as a substitute, Cora hit .243 and was part of four teams that reached the playoffs, including the 2007 Red Sox team that won the World Series.
San Diego began this season with high expectations after a series of major offseason moves, but the Padres fired manager Bud Black after a 32-33 start. Pat Murphy, who was the manager of the club's Triple-A El Paso team, was appointed on an interim basis but was not considered to continue as manager in 2016.