In other words, if the Astros decide to hire a manager who is currently on the staff of a team that makes the playoffs, they'll have to wait until that team's season is complete before announcing the choice.
"They wouldn't come on board until everything's over," he said.
Astros president George Postolos and general manager Jeff Luhnow accompanied Crane to St. Louis, but it's not known if they were planning to conduct any interviews while here.
"We're not talking about who we're interviewing," Crane said.
What is known is Red Sox bench coach Tim Bogar will interview for the Astros' full-time managerial opening on Wednesday in Tampa, a source told MLB.com. The Red Sox are in the middle of a series against the Rays in St. Petersburg.
Bogar will be the fifth known candidate to interview. Former Padres and Phillies manager Larry Bowa, Nationals third-base coach Bo Porter, Rays bench coach Dave Martinez and Astros interim manager Tony DeFrancesco also have interviewed.
But Bowa is out of the running after telling FOXSports.com he will not be the next manager of the Astros, saying he and Luhnow agreed it's a younger man's job.
"Jeff and I both were under the understanding that long-term it should be a younger guy -- we both agreed on that," Bowa told the website. "The interview was really professional. Jeff has his ducks in a row. It's just going to take some time."
Crane said he's pleased with the pool of candidates the Astros have interviewed.
"We've gotten to look at some good people," he said. "We talked to a lot of different guys in different organizations, and we're doing a pretty extensive interview with Jeff, Craig [Biggio], [special assistant] Enos Cabell, some of Jeff's staff, George and myself," Crane said. "We're doing a good job of seeing what we need, who we need and what fits best for us."
Bogar has been on the Red Sox's staff since the 2009 season and is a former manager in the Astros' Minor League system. He began his managerial career in '04 with the rookie-league Greeneville Astros, and the team went 41-26 and won the league title. Bogar managed in Class A Lexington the next year and was named South Atlantic Manager of the Year.
The Indians hired Bogar in 2006, and he led their Double-A Akron affiliate to the Eastern League title and was named the league's Manager of the Year. Bogar, 45, was a shortstop who played nine years in the Major Leagues, including four years with the Astros from 1997-2000.
Crane said DeFrancesco impressed in his interview last week.
"He interviewed very well," he said. "We were really impressed with him."