The 34-year-old Dunn, who has 460 career home runs, is in the last year of a four-year, $56 million deal with the White Sox. He is batting .220 with 20 homers, 54 RBIs and a .340 on-base percentage this season.
Because of a no-trade clause, Dunn has the power to pick which team he wants to finish this season with, and clearly, Oakland is a team with great need right now.
The White Sox also had conversations Sunday with the Los Angeles Dodgers about Dunn, according to sources.
Dunn could be a designated hitter for Oakland but would be more limited in his role with the Dodgers.
Dunn is expected to signal his choice some time Sunday. In order for a player to be eligible for a postseason roster, he must be a member of the playoff team by Aug. 31, which is why the Athletics, Dodgers or some other team must add Dunn on Sunday in order to have him available for the postseason.