McLane downplayed the window, which began on Jan. 1, saying it wasn't an indication that a sale of the team is imminent, and maintained that he's not actively trying to sell the team.
McLane didn't name the suitor, who is trying to form a group to purchase the club, but has reiterated that he's willing to listen if he's approached by a potential buyer.
"We've said from time to time [that] people come to us, and they asked, 'If we can raise a certain amount of money, would you be interested in selling the Houston Astros?' And I said, 'Sure,' " McLane said. "We gave them an exclusive window."
McLane said that despite the exclusive negotiating window, he doesn't have any other parties interested in buying the team. He revealed last month that he had a handshake agreement with Houston businessman Jim Crane following the 2008 season to sell the team, but the deal fell through because of Crane's concerns about the economy.
"This is nothing different than we've talked about before," McLane said on Monday. "I wasn't talking to anybody else."
Since he purchased the Astros, McLane has taken the franchise to new heights, including six postseason berths and the team's first World Series appearance, in 2005. The Astros moved into Minute Maid Park in 2000 and last year celebrated their 10th season in the downtown ballpark.
Last season the Astros had a club-record payroll of approximately $107 million and finished in fifth place in the National League Central. McLane said that this year's payroll will be around $95 million.
McLane said that he was approached in 2007 by George Postolos, former president and CEO of the NBA's Houston Rockets, about selling the team to Crane. Postolos left the Rockets in 2006 to form a group that helps with the acquisition of sports franchises.
But McLane said that he and Crane shook hands and agreed on a price. Crane, the owner of Crane Capital, tried to buy the Chicago Cubs and Texas Rangers last year.
"In the last five or six years, a lot of people talked [about buying the team], and 99 percent of time it never amounts to more than one conversation," McLane said last month.
Brian McTaggart is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.