If the White Sox players were hoping that the trade rumors surrounding the team would end once spring camp started they are finding out that they were very wrong.

It’s obvious that this roster might have a short shelf life if the standings aren’t to the liking of general manager Ken Williams.

That’s why the Gavin Floyd trade rumors with Toronto continued to circulate, and that’s also why reliever Matt Thornton continued to hear his name swirling around.

It’s pretty simple for several of the White Sox veterans: Win early or start packing.

“Other teams want me, they want Gavin, they want different pieces from our team,” Thornton said. “Well, that means you’re pretty good ballplayers and you’re talking about contenders that are going to go after you.

“This year, it’s all about winning ballgames. We go out and start winning ballgames, no one is going anywhere. Who knows what happens if we start struggling.”

It’s obvious what happens.

Floyd has $7 million coming with a club option next season, and is the best bargaining chip the White Sox have from a starting pitching standpoint.

Catcher A.J. Pierzynski is $6 million this year and a free agent next season.

Then there’s Thornton, who is owed $12 million on his contract through 2013, with a $1 million buyout in 2014. Like Floyd, he was shopped around by the White Sox in the offseason.

Thornton says all the right things about his stay on the South Side, but he also wants to win.

“I’m to the point in my career where I just want to win,” Thornton said. “I want to win ballgames, man. I’m tired of last year, being under .500, missing the playoffs the last three seasons in-a-row.