Dunn, an investor in the Oscar-nominated film "Dallas Buyers Club," has an invitation to attend the Academy Awards show Sunday in Los Angeles. Dunn has a cameo role as a bartender in the movie, which was produced by his friend Joe Newcomb, founder of Truth Entertainment.
"I'm still debating whether I want to do it," Dunn said from Chicago's spring training camp in Glendale. "I don't know yet, but the offer is there. How many opportunities do you have to go to the Oscars? But if it's any sort of big deal with the team, I won't go."
That doesn't appear to be the case. In an email to ESPN.com, general manager Rick Hahn said, "We told him it wouldn't be a problem if he wanted to head out there for a night."
Manager Robin Ventura also gave his approval, saying Dunn can work out in the morning, fly to Los Angeles after the workout and then take the following day off. Players get a floating day off during camp, but Dunn joked that he wasn't sure about using it so early in the spring.
Ventura wasn't worried about setting a precedent since he wasn't sure he would ever manage another player involved in an Academy Awards-nominated film.
"You're looking first at how many people get a chance to do that and actually be a part of it, not just go just to go, but be a part of something that has a chance to do something special," Ventura said. "Even the next day, I'd rather have him not worry about the next day and have him catch up after that."
Dunn said he has a "ride" to Los Angeles, meaning that he has access to a private plane.
Dunn has been a disappointment on the field for the White Sox since signing a four-year, $56 million deal before the 2011 season. Asked about fans who might have objections to him attending a non-baseball event during spring training, he said that was the furthest thing from his mind.
"No, I don't think that would be that big of an issue," Dunn said. "But again, if it was, I care about these 25 guys here and the coaches."
Newcomb, formerly a pitcher in the Toronto Blue Jays organization, used to throw to Dunn in the offseason. He lobbied Dunn to accept a non-speaking part in the movie as bartender Neddie Jay.
Dunn said it was an education watching Matthew McConaughey, Jared Leto and the other actors work. McConaughey and Leto are nominated for Oscars, and Dunn predicted they're a "lock" to win.
"Those guys are in character and they're so focused. I wish everybody could kind of experience that," Dunn said. "They'll do a take that's perfect and the director will say, 'Let's do another take.' What do you get, more perfect? Those guys aren't griping or anything. They're so professional. I'm really glad I got to see that. It's pretty amazing."
For what it's worth, Dunn said he owns a tuxedo, so he won't have to buy or rent one if he decides to go to L.A.
"I'm pretty much a T-shirt, boots and blue jeans guy," Dunn said. "I have a tux. I'm just not sure I could still fit in it or not."