Citing unidentified sources, SI said the team could announce the move as soon as Friday.
Alderson met with the Mets' ownership group Tuesday, and the team said it wouldn't comment any further on the search until it is ready to announce its next GM.
Contacted by The Associated Press on Tuesday night, Mets spokesman Jay Horwitz said he had no new information to provide. Messages left for chief operating officer Jeff Wilpon were not immediately returned.
Alderson, the former president of the Oakland Athletics and chief executive officer of the San Diego Padres, met Tuesday with Mets controlling owner Fred Wilpon, his son Jeff, and club president Saul Katz.
Alderson and former Arizona Diamondbacks general manager Josh Byrnes were brought back for a second round of interviews this week as the two finalists to replace Omar Minaya, fired along with manager Jerry Manuel after the team's second consecutive losing season.
The club has said its new GM will lead the search for the next Mets manager.
Byrnes met with Mets ownership Monday. He and Alderson had initial interviews earlier with Jeff Wilpon and lower-level management.
Alderson, who turns 63 next month, was Oakland's general manager from 1983-97. He built power-packed teams that won three straight AL pennants from 1988-90 and a World Series title in '89. He currently is in charge of baseball's efforts to reform operations in the Dominican Republic.
Major League Baseball discourages teams from making major announcements during the World Series. Game 1 between the Texas Rangers and San Francisco Giants is Wednesday night, with the first off day in the Series coming Friday between Games 2 and 3.
New York also interviewed Allard Baird, Dana Brown, Rick Hahn and Logan White for its GM position.
Well-respected among MLB executives, Alderson was executive vice president for baseball operations in the commissioner's office from 1998-2005. He served as CEO of the Padres from 2005-09.