Walker interviewed with the Braves and San Diego Padres over the last 10 days.
He resigned his position after 8½ seasons with the White Sox.
Walker played nine seasons (1982-90) with the White Sox and part of one year (1990) with the Baltimore Orioles, hitting .260 with 113 home runs and 444 RBIs.
The White Sox have yet to replace Walker.
Bruce Levine covers baseball for ESPNChicago.com and ESPN 1000.