CHICAGO -- White Sox management on Monday refuted claims by former reliever Keynan Middleton that the downtrodden team had a culture with "no rules," allowing a rookie reliever to regularly fall asleep during games and other players to miss meetings and practices.

Middleton, dealt to the New York Yankees for minor league pitching prospect Juan Carela just before the Aug. 1 trade deadline, made the statements in an ESPN report published Sunday.

Before Monday's game against the Yankees in Chicago, White Sox general manager Rick Hahn and first-year manager Pedro Grifol said Middleton's statements were inaccurate. But both admitted their disappointing team had faced its share of internal issues, centering around building a winning culture.

"I've been talking about culture here since day one and brought it up again about three or four weeks ago," Grifol said. "I feel like we're not even close to where we need to be, but we're heading in the right direction."

The White Sox, expected to contend, entered Monday at 45-68 and in fourth place in the American League Central.

Hahn emphasized that no reliever had been dozing in the bullpen, while adding the White Sox have a position player with a serious sleep disorder who is permitted to take naps in the clubhouse per medical direction.

"I was surprised to see the report this morning," Hahn said. "At no point during the course of the year had there been a reliever sleeping in the bullpen during that game. That's just wrong."

Hahn and Grifol said there have been times when players have violated team rules, but they faced discipline that wasn't disclosed under a typical baseball policy of "what happens in the clubhouse stays in the clubhouse."

Hahn said Middleton was one of those players.

"Quite frankly, it's a little bit ironic that Keynan's the one saying this, because my last conversation with him face-to-face was a week ago in the clubhouse where he sought me out to apologize for his unprofessional behavior Pedro had called him out on," Hahn said. "At the time I figured that was a one-off."

Hahn said Middleton told him before the trade to New York that he might want to return to a Chicago as a free agent after the season.

When told of the White Sox management's replies before Monday's game, Middleton stood by his original statements.

"I said what I said and I stand on that," the 29-year-old right-hander said. "I honestly don't want to comment on it any more.

"Right now my sole focus is being a Yankee, my future being a Yankee moving forward and making the playoffs and all these things."