Geivett is a former special assistant to the GM with Tampa Bay and headed Montreal's farm system for three years.
Astros president and CEO George Postolos had no comment.
Houston owner Jim Crane, who took control of the club a week ago after purchasing it from longtime owner Drayton McLane, has spoken of his admiration about the way the two-time defending AL champion Rangers rose to prominence through scouting and player development. The Astros are trying to follow a similar blueprint.
Another Rangers executive, senior director of player personnel A.J. Preller, is also reportedly on the Astros' radar as they try to fill a position left vacant when Ed Wade was dismissed following a club-record 106 losses in 2011. Astros ownership loves the way the Rangers built their franchise by focusing on player development, so it only stands to reason that Preller might be in the discussion.
David Gottfried, the Astros' assistant GM, has been named interim GM, and he said he was told by Postolos he would remain in that role through at least the Winter Meetings. That would give the Astros plenty of time to interview potential candidates in Dallas next week.
Here is a list of some other potential GM candidates the Astros may took a look at:
Gerry Hunsicker: This would be a popular choice among fans, who still remember Hunsicker's successful nine-year tenure as GM of the Astros that ended in 2004. He's the senior vice president of baseball operations with the Rays, but still has a home in Houston.
Peter Woodfork: He's a former D-backs assistant general manager who works in Major League Baseball operations under Joe Torre. He's a Theo Epstein disciple, having worked under him with the Boston Red Sox.
J.J. Picollo: As the assistant GM of the Royals who oversees both the player development and scouting departments, Picollo has plenty of experience listening to a variety of opinions. He was the Braves' farm director before GM Dayton Moore brought him to Kansas City five years ago.
Jeff Kingston: The assistant GM in Seattle, Kingston worked with Kevin Towers in San Diego before being hired away by the Mariners.
Billy Eppler: An assistant GM with the Yankees, Eppler interviewed recently for the Angels' vacant opening and is considered a solid candidate to be a GM in the future.
Logan White: An assistant GM with the Dodgers, White's in charge of amateur and international scouting for GM Ned Colletti. In 2007, he interviewed with the Astros before Wade was hired.
De Jon Watson: The head of player development with the Dodgers, Watson interviewed for the Orioles' vacant GM position in October before withdrawing. He interviewed last year with the D-backs for the job that eventually went to Towers.
Rick Hahn: The highly respected assistant GM of the White Sox, Hahn is a former sports agent who used to work for Jeff Moorad. Hahn interviewed previously for GM jobs with the Cardinals, Mets and Cubs.
Al Avila: The assistant GM of the Tigers, Avila is more of a veteran scout, in the mold of Colletti, but he has a very good track record. He's the father of Tigers All-Star catcher Alex Avila and son of longtime Dodgers scout and executive Ralph Avila.
Allard Baird: If the Astros find themselves looking for a veteran GM not named Hunsicker, Baird could be their guy. He's a strong talent evaluator who turned down the Orioles earlier this year. The former Royals GM now works for the Red Sox as vice president of player personnel and pro scouting.
Other young executives who could get a look: Damen Oppenheimer, Yankees; John Coppolella, Braves; Kyle Stark and Tyrone Brooks, Pirates; and Mike Hazen, Boston Red Sox.