"This is what I wanted to avoid," Dunn said on Tuesday.
The Chicago Sun-Times reported on Tuesday, citing multiple unnamed sources, that the White Sox covet the big left-handed-hitting first baseman and have explored trade possibilities. The Angels are also reported to be interested.
Dunn, who hit 38 homers for the Nationals last season, is in the final season of a two-year contract worth $20 million that he signed as a free agent. He went into the middle game of the Nationals' three-game set with the Braves batting .276, with 17 homers and 47 RBIs.
"I want to stay," he said. "I don't want to talk about maybe going somewhere else. This gets old. I don't want to be a part of it. The only thing I know [is that] I'll be playing somewhere. I hope it's here."
General manager Mike Rizzo stayed firm in his policy of not talking about potential trades.
"There's a new rumor every day," Rizzo said. "I'm not going to address any of them. It's not fair to anybody. We're not going to do it."
The Nationals and Dunn's representatives have been talking about a contract extension since Spring Training. So far there has been no apparent progress.
"I've talked to his agent on several occasions, so we're communicating," Rizzo said.
"I really don't know what's going on," Dunn, 30, said. "I'm not involved."
The first baseman did make it clear that should he be traded to an American League team, he doesn't want to be a designated hitter.
"I'm not ready to do that," he said. "Maybe in four or five years, but not now."
The 6-foot-6 Dunn has never been known for his defense, whether playing the outfield or first base. But he reached 40 homers in five consecutive seasons before falling just short a year ago, when he hit .267 and drove in 105 runs.