Garner said on Monday afternoon that club officials told him he was still in the running for the job, even though he has not yet been asked to return for another interview.
"I've been told I'm still in the mix," Garner said.
"We did have four good candidates and now we have three really excellent candidates, and the next couple of days we'll either visit them in person or communicate with them [via telephone]," Astros owner Drayton McLane said while traveling to Temple, Texas, from Austin.
McLane said he'll be in Houston on Tuesday and Wednesday and said to expect a manager in place by the end of the week.
Mills, 52, managed 11 seasons in the Minor Leagues with the Chicago Cubs (1987-92), Colorado Rockies (1993-96) and Los Angeles Dodgers (2002), moving into managing immediately upon the completion of his playing career. He's coached 11 years at the Major League level, including the last six as Boston's bench coach under Terry Francona.
Wade has tremendous respect for Francona and said dismissing him as manager of the Philadelphia Phillies was the biggest mistake of his professional career. Mills and Francona were teammates and roommates at the University of Arizona.
Mills played four seasons in the Major Leagues for the Montreal Expos, hitting .256 in 106 career games. He spent some time playing in the Astros' Minor League system, but is probably best remembered by Astros fans for being Nolan Ryan's 3,509th strikeout victim, lifting Ryan past Walter Johnson as baseball's all-time strikeout king in 1983.
In addition to the Red Sox, Mills has also spent time on Montreal's Major League coaching staff, as well as serving as an advance scout for the Cubs.
Clark, 47, compiled a 432-405 record in six seasons as manager in the Minor Leagues, including four seasons in the Astros organization. He went 207-212 in three years at Double-A Corpus Christi and won the Texas League title in 2006 and managed at Triple-A Round Rock in 2008.
A former outfielder who ended his 13-year playing career with the Astros in 1998, Clark hit .264 with 62 home runs and 284 RBIs in 905 career games. He was originally selected by Cleveland in the first round of the 1983 First-Year Player Draft and spent time with the Indians (1986-89), Chicago Cubs (1990, 1997), Kansas City Royals (1991), Pittsburgh Pirates (1992-96), Los Angeles Dodgers (1996) and Astros.