So, even after producing his first All-Star appearance during the 2010 campaign, Thornton joked about whether the White Sox truly wanted to have him around when he waited three weeks this October for his 2011 option to be exercised.
"Last year was two days. This year was three weeks," Thornton told MLB.com in comedic tones during a phone conversation from his Arizona home on Tuesday. "I wondered if they didn't like me anymore.
"I've really enjoyed my time in Chicago. I'm looking forward to my sixth season there. I'm looking forward to helping the team."
Thornton, 34, will earn $3 million for the upcoming season in the final year of his three-year, $3.25 million contract agreed to before the start of the 2007 season, which included team options in the past two seasons. Catcher Ramon Castro also had his 2011 option exercised Tuesday at $1.2 million, while right-handed reliever Carlos Torres was released to allow him to pursue an opportunity to pitch in Asia.
Castro figures to resume his highly successful reserve role behind the plate, whether free agent A.J. Pierzynski returns to the team, rookie Tyler Flowers is given the starting job or the White Sox go in another veteran direction. The bullpen role for Thornton stands as a bit less defined.
The hard-throwing southpaw certainly will be featured in a late-inning capacity. But the White Sox franchise leader with 100 career holds could be moved into the closer's job, depending on how the offseason plays out under general manager Ken Williams' watch.
After posting a 5-4 record, 2.67 ERA and a career-high eight saves in 61 relief appearances during the 2010 season, Thornton certainly seems ready to move to the last line of White Sox pitching defense.
"I've done everything to deserve that chance," said Thornton, who fanned 81 over 60 2/3 innings last year. "I've done well in the ninth inning. In my career, I've had one ninth-inning blown save, and that was a solo home run to [Nick] Swisher, a one-time thing.
"My career numbers have gotten better as I've gotten older," said Thornton, who has posted three straight seasons with ERAs under 2.75 for the White Sox. "I would love the opportunity to be the White Sox closer. I'll be prepared for anything they bring my way."
One blip in Thornton's healthy overall run with the White Sox came from Aug. 18 to Sept. 5, when he was placed on the disabled list with inflammation in his left elbow. Working more than one inning in each of his last six September and October relief appearances, while striking out 11, giving up one hit and not allowing an earned run, certainly proved that he had no lasting effects from the injury. He has not received any treatment on the area during the offseason.
Pedro Feliciano, Matt Guerrier and Arthur Rhodes join Thornton as the only four relievers to record at least 20 holds in each of the last three seasons. Thornton has a 2.70 ERA and 245 strikeouts over 200 1/3 innings during this span.
His 12.02 strikeouts per nine innings and his 12.9 inherited runners scored percentage topped all American League relievers in 2010. Thornton ranked in the Top 10 in strikeout-to-walk ratio (4.05), holds (21) and opponents average (.191).
Left-handed hitters batted just .175 (17-for-97) against Thornton, who became the first White Sox hurler to top AL relievers in strikeouts since Keith Foulke in 1999. All of those numbers make Thornton valuable in a setup role, whether he's pitching in the eighth against the heart of the opposition's batting order or working two innings to get to the closer.
That value could easily translate into a closer's opportunity. Much of that decision centers on how Williams and the White Sox decide to shape the rest of the bullpen.
Bobby Jenks, who has been one of the game's top closers since assuming the job during the 2005 World Series championship season, is arbitration-eligible. The right-hander could become a non-tender candidate after earning $7.5 million during a 2010 campaign plagued by freak injuries.
J.J. Putz is also coming off a strong bounce-back year from an injury-shortened 2009 with the Mets, and he could figure into the equation as a White Sox free agent.
Thornton is certainly not campaigning for the job, appreciating what Jenks has accomplished, in particular.
If the opportunity presents itself, though, Thornton is ready.
"I've been ready to close for the last couple of years," Thornton said. "But we had someone like Bobby there, and he does a heck of a job as a closer.
"You are talking months away from worrying about that decision. But if the opportunity presents itself, I would love that opportunity."
Scott Merkin is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.