Machado agreed to a 10-year, $300-million deal with the Padres on Tuesday, ending the White Sox's pursuit.
The White Sox's offer has been reported at eight years and $250 million guaranteed, with vesting options at $35 million for 2027 and 2028 -- figures that Hahn referred to as "generally" accurate in an interview with Laurence Holmes on 670 The Score on Wednesday. However, Hahn denied a report that the White Sox as an organization are opposed to opt-out clauses, which Machado did secure at the end of his fifth year with the Padres.
"Absolutely not," Hahn said. "There's not an organizational philosophy. You make the assessment based on the individual give-and-take within the negotiations."
Hahn also denied that the White Sox weren't capable of reaching the $300-million mark with Machado or any potential free agent while stressing the organization won't be capped at a certain threshold in future negotiations.
The White Sox made their offer to Machado at the value they believed was fair.
"There is no magic limit on where we would go (with Machado)," Hahn said. "You got to make the evaluation based on every individual player. They're obviously all different. They got different risks. They got different upside, different benefits and fits to the club.
"In this deal at the end of the day, we weren't comfortable -- as (executive vice president Kenny Williams) alluded to -- we weren't going to get to that ($300 million) level, but we obviously tried to address some other concerns that the player had in order to make the offer appealing. But there is no limit. It's about making an assessment about the individual player, the risk that that player brings and what potential alternatives exist in the future for that money."
The White Sox last met Monday afternoon with agent Dan Lozano and Machado's party, with the organization bringing chairman Jerry Reinsdorf and Williams. Their final offer was on the table.
Hahn and the White Sox believed their offer was enough to entice Machado to join them in Chicago. The Padres' proved to be better in Machado's view.
"I don't think it would be fair to them to say, 'Hey, you got X. Give us the chance to go to X plus one,'" Hahn said. "But we did have the sense, and we had very candid conversations about where he thought it was going and how we would go about trying to make him a White Sox. The ultimate contract offer was based on those conversations about what the priorities were.
"This is free agency. These guys work extremely hard to get to a point where they can make a decision based on whatever they want. It can be guaranteed dollars, it can be upside, it can be 'my wife has a cousin there who shes very close with, and we want to be there.' There's a lot of moving pieces that ultimately lead to these decisions. I don't think there was any specific thing that we necessarily refused to do that therefore torpedoed the whole situation."
Hahn addressed reporters twice Tuesday -- first from the White Sox's spring training camp in Glendale, then later at a pre-scheduled MLB general managers availability. He spoke of the Machado situation plenty and expressed the frustration of it all -- which he admitted was still present Wednesday.
"I don't take a great deal of solace in trying hard when you come up short," Hahn said. "We work in pro sports. It's pretty binary, it's win (or) lose. You either get it done or you don't. We didn't get it done. So I understand the frustration.
"Even though we're disappointed by the failure, this isn't the last time we're going to try to do it. That money's going to get spent. When it gets spent, I'm not sure. How it gets spent, I'm not yet sure, other than it's going to get spent similar to the fashion we tried to spend it earlier in the week, and that's to put us in the best position long term to win multiple championships."
With Opening Day just more than a month away, it remains to be seen whether the White Sox will aggressively pursue another free agent with the money they still have after missing Machado.
Could Hahn and his organization rally with an offer for the other superstar that has been available, Bryce Harper?
"There is an open line of communication," Hahn said. "(Agent Scott Boras) and I have very direct and candid dialogue whenever we speak. We're always available to each other."