The right-hander, who was acquired from the Toronto Blue Jays just days before the July 31 non-waiver trade deadline, wasn't at his best after the trade, going 1-2 with a 5.09 ERA after the deal, but did have 20 strikeouts in 17 2/3 innings. Frasor made $3.5 million in 2011.
The Oak Forest High School graduate admitted late in the season that he struggled with the pressures of coming back to pitch for his hometown team.
The White Sox are looking for the right-hander to return to the form he showed in Toronto since 2004. Including his numbers with the White Sox the last two months of the 2011 season, Frasor has posted a 3.74 ERA in his career with 446 strikeouts in 475 appearances.
Doug Padilla covers the White Sox for ESPNChicago.com and ESPN 1000.