Postolos wouldn't confirm individual candidates.
"It's a process of identifying people who are a fit and getting permission to talk to them and then getting in front of them and getting a sense of them," he said.
The Rays released a statement Monday night from team president Matt Silverman which confirmed Friedman, a Houston native who received permission to interview with the Astros, wasn't interested in the job.
"Andrew chose not to be a part of the Astros' process," the statement read. "It is in no way a reflection on the Houston organization."
Postolos didn't acknowledge Friedman's decision and said he didn't want to put a timetable on the hiring of a GM, though it appears unlikely the club will have one in place before it leaves Dallas.
"We are proceeding with all deliberate speed," he said. "We're very eager for the process to come to a conclusion, but the key thing for us is to make sure we find the right person. We continue to be impressed with how many smart, capable people there are in baseball -- not only the candidates we're talking to, but industry veterans and other people who have been in this situation before, owners and senior executives. Baseball is a fraternity, and they're very willing to provide information to us about the candidates, about the process."
Postolos said the Astros are focused on GM candidates who have a strong track record in scouting and player development, saying it's "critical" for the team. The Astros want to get competitive on the field with their own prospects before spending in free agency.
The Astros have already made significant inroads in improving their farm system by trading Lance Berkman and Roy Oswalt last year and Hunter Pence and Michael Bourn at the Trade Deadline this year. The trades of Pence and Bourn netted eight players in return, five of whom are among the team's top prospects.
Postolos wants to make sure the new GM stays the course of building through player development.
"We've seen a number of very strong candidates," he said. "We've been very pleased by that. A lot of times, you've seen candidates from two different pools. You see candidates that come up as assistant general managers who are focused on roster construction and candidates who come from a pool of people who are experienced in scouting and player development. Because of where our franchise is and our priorities, we tend to be focused in that scouting and player development pool."
Meanwhile, the club continues to shop veteran pitchers Wandy Rodriguez and Brett Myers and outfielder/first baseman Carlos Lee. The Astros would be willing to take back money on trades involving Myers and Lee, but not Rodriguez, according to a Major League Baseball source.
Lee is scheduled to make $18.5 million next year, the final year of his six-year, $100 million deal. He has a partial no-trade clause, meaning he has given the Astros a list of teams to which he could be traded. Rodriguez is due $10 million next year, $13 million in 2013 and would get $13 million in '14 if he changes uniforms. Myers is due $11 million in '12 and $10 million in '13, if his club option is picked up.
Postolos said interim general manager David Gottfried has the go-ahead to make any deals that would benefit the club without waiting for a full-time GM to be in place.
"We are open for business," he said. "David Gottfried is in place as interim GM and has the authority to go out there and make moves to improve the team. I think oftentimes the foundations are being laid, but if there's an opportunity that fits with our plan and where we're trying to go, we're absolutely prepared to do it."
Gottfried, who's not a candidate for the full-time GM job, said he and his staff have been networking with other clubs to try to find possible fits.
"I don't think it's fair to talk about the amount of interest or lack of interest, but we've talked to a lot of clubs and seen what they're looking for," he said.
The Astros' top priority on the field is finding a starting shortstop following the loss of Clint Barmes in free agency. Angel Sanchez could play the position, but he's not considered to be a viable full-time shortstop.