Mills and Bogar are the final two of 10 candidates interviewed by the Astros since last Wednesday. Houston is looking for a replacement for Cecil Cooper, who was fired on Sept. 21.
The 52-year-old Mills has been Boston's bench coach for the past six seasons. He previously managed minor league affiliates for the Chicago Cubs (1987-92), Colorado (1993-96) and Los Angeles Dodgers (2002). He served as current Boston manager Terry Francona's bench coach in Philadelphia from 1997-2000 before joining him in Boston.
The 42-year-old Bogar finished his first year as Boston's first-base coach. He joined the Red Sox from Tampa Bay, where he was the quality assurance coach in 2008.
Bogar has past ties to the Astros. He managed their rookie league affiliate in 2004 and their Class A team in Lexington in 2005. Bogar also played for the Astros in four of his nine major league seasons (1997-2000), helping Houston win three NL Central titles. He also played for the New York Mets (1993-96) and Los Angeles Dodgers (2001).
The Astros also interviewed interim manager Dave Clark; minor league field coordinator Al Pedrique; former Milwaukee manager Ned Yost; San Diego hitting coach Randy Ready; former Seattle and Arizona manager Bob Melvin; former Washington manager Manny Acta, former Astros manager Phil Garner and Philadelphia bench coach Pete Mackanin.
Astros officials say they will trim the list to an undetermined number this week, then conduct a second round of interviews. They've set no timetable for picking the finalists or a new manager.