The 28-year-old Jenks went 3-4 with a 3.71 ERA and 29 saves in 35 chances for the White Sox in 2009, falling one save short of his fourth consecutive 30-save season.
Quentin, meanwhile, batted .236 with 21 homers and 56 RBIs in 99 games this past season, a year in which he spent nearly two months on the disabled list with plantar fasciitis in his left foot. The 27-year-old is coming off a season that saw him make the American League All-Star team and win a Silver Slugger Award.
Arbitration-eligible players without a 2010 contract will exchange figures with their respective clubs on Tuesday, and arbitration hearings will be scheduled Feb. 1-21. Clubs can still negotiate with their players from the time they exchange figures until the respective hearings.
The White Sox haven't gone to arbitration with a player since 2001.
Alden Gonzalez is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.