The team has already interviewed former Marlins general manager Larry Beinfest and also Dodgers vice president of amateur scouting Logan White.
New York Yankees assistant general manager Billy Eppler is expected to interview this week.
San Diego executive chairman Ron Fowler and team president and CEO Mike Dee have conducted the interviews. Dee said Wednesday that he expects the new general manager to be on the job sometime after the July 31 non-waiver Trade Deadline.
The list of general manager candidates could see additions and subtractions. Two candidates -- David Forst of the A's and Jason McLeod of the Cubs -- have declined interviews. Forst is the assistant GM while McLeod, who previously worked for the Padres, is the Cubs' scouting director.
San Diego's senior vice president of baseball operations, Omar Minaya, has said he will not ask for an interview. Current Padres assistant general manager A.J. Hinch is a viable candidate for the job. He's handling the day-to-day operation of the big league team.
Two assistant general managers -- Mike Hazen of the Red Sox and A.J. Preller of the Rangers -- have indicated that they'll interview for the job.
A CBSSports.com report Wednesday said the Padres would interview Kim Ng, a former assistant GM with the Yankees and Dodgers, who is the senior vice president of baseball operations for Major League Baseball.
As for Montgomery, 44, he became the director of scouting for the D-backs in 2010. In 2009, he turned the Padres down for their scouting director opening.
Corey Brock is a reporter for MLB.com. Keep track of @FollowThePadres on Twitter. This story was not subject to the approval of Major League Baseball or its clubs.