Beckham said before Tuesday's game that he was told by White Sox management that he won't be going anywhere at the trade deadline.
"I've been pretty much told that I will be OK and will be in a White Sox uniform after July 31," Beckham said. "I'm not too worried about it. I wasn't too worried about it. I think it's just kind of fun for all the speculation, but that's about all it is usually."
An ESPNChicago.com report earlier Tuesday said that the Washington Nationals' request to trade Dunn for Beckham straight up was rejected by the White Sox. According to the same report, Dunn could still be moving to the South Side for a package of Daniel Hudson and one of three top prospects: catcher Tyler Flowers, outfielder Jordan Danks or injured infielder Brent Morel.
"I have nothing but the best stuff to say for the White Sox," Beckham said. "They have been in my corner all year and they didn't have to be. They could have given up on me. Hopefully I will be able to reward them for the rest of the year. It feels good. It's nice to know you're wanted and I have really enjoyed my time here."
Knowing that he is valued more by the White Sox than having Dunn's power potential could potentially put pressure on the young second baseman to produce.
"I can't worry about that," Beckham said. "If I don't play well, I can't say, 'Well, maybe Adam Dunn would have done better.' It is what it is. I will go out and play. It's been an up and down year but I feel like I'm on the rise."
Doug Padilla covers the White Sox for ESPNChicago.com.