Team executive chairman Ron Fowler and CEO and team president Mike Dee expect to have Red Sox assistant general manager Mike Hazen, Yankees assistant general manager Billy Eppler and Kim Ng, senior vice president of baseball operations for Major League Baseball, back for second interviews.
Fowler said recently that he hopes to have a general manager hired by early August.
Preller is in his 10th season with the Rangers and has been one of general manager Jon Daniels' most trusted lieutenants. From 2010-13, he was in charge of the Rangers' professional, international and amateur scouting and helped rebuild the farm system.
The Padres are looking for a replacement for Josh Byrnes, who was dismissed by the team on June 22.
A total of eight candidates had initial interviews -- former Marlins general manager Larry Beinfest, Dodgers vice president of amateur scouting Logan White, D-backs scouting director Ray Montgomery, Eppler, Preller, Hazen, Padres assistant general manager Josh Stein and Ng.
Six candidates declined to be interviewed, the latest being current Padres assistant general manager A.J. Hinch, who is presiding over the day-to-day operations of the big league team.
The five others who declined interviews: David Forst of the A's, Mike Chernoff of the Indians, Jason McLeod of the Cubs, Michael Girsch of the Cardinals and Padres senior vice president of baseball operations Omar Minaya.
Forst, Chernoff and Girsch are assistant general managers. McLeod, who previously worked for the Padres, is the Cubs' scouting director.
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.