Crane said Monday there's a possibility Clemens could pitch this season for the majors' worst team.
"We haven't heard from Roger, so that's still up in the air," he said.
The last-place Astros started a weeklong homestand on Monday that includes three games against the Cubs and four against the Phillies. Their only remaining home games after this stretch are against the Pirates and the Cardinals -- two teams in postseason contention.
Crane said he would not pitch the seven-time Cy Young Award winner against a contender, which leaves this week as the only option.
But Clemens said Monday night the only way he would pitch this season was against a team in contention.
"I can tell you right now and they would know, too, that if I was going to go do it, I am going to pitch against a contender, that's who I want to knock out," Clemens told Houston television station KRIV. "Why would I want to waste my time running around and getting in shape. I get over to Minute Maid (Park), I'll crank it up and get it over 90 for a contender. We'll knock them right out of the playoffs. That would be the fun. Pitching against somebody that's not in contention wouldn't be any fun for me."
"It's not going to happen."
A message was left seeking comment from Clemens' agent, Randy Hendricks.
Crane wouldn't say whether the team will reach out and try to entice Clemens to return to the majors for the first time since pitching for the Yankees in 2007.
"We're just going to sit tight," Crane said. "We'll wait and see if he calls us, but we might call him, who knows?"
According to the Elias Sports Bureau, if he does play for Houston, Clemens would become the seventh player in baseball history to play a game at age 50 or older. Satchel Paige and Jack Quinn are the only players ever to throw a pitch in their 50s.
Clemens pitched 3 1/3 scoreless innings in his first start for Sugar Land of the independent Atlantic League, and didn't allow a run in 4 2/3 innings in his second start Friday.
When asked about pitching for Houston this season, Clemens said Friday he didn't see it happening because of the time it took him to recover from his first start.
The Astros sent a scout to watch both of his outings. General manager Jeff Luhnow said he didn't have any new information on the subject.
"Right now we have a six-man rotation and we've lined up that rotation for the rest of the year, so I'm not expecting any changes," he said. "The words that I've heard Roger say suggest that that's not front and center in his mind. At this point I'm not expecting it."
Clemens earned $160 million and won 354 games in a 24-year career with the Red Sox, Yankees, Blue Jays and Astros. His 4,672 strikeouts are third-most and he was selected for 11 All-Star games.
Clemens had two great seasons with the Astros after he turned 40, going 18-4 with a 2.98 ERA in 2004 to win his record seventh Cy Young Award. He was 13-8 with a career-low 1.87 ERA in 2005.
The Rocket's fastball was clocked at as high as 88 mph, and he also threw curves and splitters in his starts for the Skeeters.
But it seems he isn't sure if his stuff is major league ready at this point.
"I don't think I could make an impact," Clemens said last week when asked about pitching for the Astros. "I think it would be fun for a lot of people, but it would take a lot of work to do and to perform the way I would want to perform. My mind says yes. My body says no."
Clemens' re-emergence with the Skeeters is the first time he has been in the spotlight since he was acquitted of charges he lied to Congress when he denied using performance-enhancing drugs.
Clemens was accused by former personal trainer Brian McNamee in the Mitchell Report on drugs in baseball of using steroids and HGH, allegations Clemens denied before Congress. The Justice Department began an investigation concerning whether Clemens had lied under oath, and in 2010 a grand jury indicted him on two counts of perjury, three counts of making false statements and one count of obstructing Congress.
He was acquitted of all the charges on June 19 after a 10-week trial and had largely stayed out of the public spotlight until signing with the Skeeters on Aug. 20.
Also Monday, Crane said the Astros are beginning the process of hiring a new manager to replace the fired Brad Mills. Crane said they have narrowed down their list to about six candidates and will begin interviews this week.
He would not name any of the candidates, but said interim manager Tony DeFrancesco would be considered.
Information from The Associated Press was used in this report.