White Sox slugger Adam Dunn may find himself in a postseason race with contenders like the Giants and Athletics looking to acquire his left-handed bat.

The San Francisco Giants and Oakland Athletics are among teams interested in acquiring Chicago White Sox slugger Adam Dunn before the Monday deadline for postseason eligibility, two sources told SI.com. A potential trade may be Dunn's final chance to experience postseason baseball.

Dunn, 34, playing the last season of four-year, $56-million contract, has indicated he may retire after this season. He has played more career games without reaching the postseason than any active player (1,976). He ranks 15th in most games without playing in the postseason since the World Series began in 1903, including the most of any player who began his career after 1972.

Why September comebacks are few and far between in MLB

​Dunn hit his 20th home run Saturday, the 460th home run of his career. Though he is hitting just .220, Dunn is valued for his power against right-handed pitching. He has hit 18 of his homers this season against right-handed pitching. Only 10 players in MLB have more.

The Giants and A's are looking to add to their offensive depth. While the Giants lead the NL in batting in August, Oakland ranks last in the AL for the month. The Los Angeles Dodgers also inquired about Dunn but a source familiar with the Dunn talks said they did not appear to be a fit.

Sunday is considered the last true shopping day before the postseason. Any player acquired beginning Sept. 1 is not eligible for postseason play, a deadline that often leads to trade activity in the 24 hours leading to it. On Aug. 31 last season the Dodgers traded for infielder Michael Young, the Pirates traded for first baseman Justin Morneau and the Red Sox traded for infielder John McDonald.