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If Paul Konerko returns to the White Sox, he can thank Adam Dunn and A.J. Pierzynski, who deferred big chunks of their new contracts, for their generous contributions.

And he can thank, in a roundabout way, reliever Scott Linebrink, whom the Sox traded to the Braves on Friday for pitcher Kyle Cofield. Even though the Sox sent $1.5 million to Atlanta with Linebrink, their savings for next season will be about $4 million.

Now it’s up to Konerko.

“I would love for Paul to return,” Dunn said Friday during an introductory news conference at U.S. Cellular Field. “I know he’s a great player and one of (the leaders), if not the leader, of this team.”

Dunn will be paid $12 million next season, $14 million in 2012 and $15 million in each of the final two years of the contract. Pierzynski will be paid $2 million next season and $6 million in 2012.

“If it helps the team win and helps the White Sox get better, then it’s really going to make me feel better because that’s all I want in the end,” Pierzynski said. “I took less money to come back, and … I feel great about it.”

“They’re putting their money where their mouth is,” said general manager Ken Williams, who kidded about looking under couches for more money to cover a payroll that will exceed last season’s but insisted the team isn’t broke.

“I heard speculation that we would have to move one of our big-salary guys, and that’s not true,” Williams said.

If Konerko does return, it means Dunn will be primarily a designated hitter, even though he has said he wasn’t ready for that role at 31.

“I don’t care,” he said Friday. “I’m to a point now where I’m on a team that has a chance to win a World Series, and I’ll do whatever they want me to do. I told Kenny the other day that I would catch, but I see they signed A.J.”

Dunn’s deal didn’t take long to complete after he declined arbitration from the Nationals on Wednesday. The Sox will give up a first-round draft choice for signing him.

“This is the No. 1 place I wanted to go,” Dunn said. “I love this city, I made that pretty clear. I come to a team already proven that it can win.

“It’s a great opportunity to not just win but to win a World Series. That’s everyone’s goal, and that’s what I want to do.”

Past speculation had Dunn winding up playing at Wrigley Field, where he posted huge numbers with the Reds. But he said Friday he wasn’t sure the Cubs were interested.

“I stay out of that; that’s business,” he said. “As soon as I found out the Sox (were interested), I was ready.”

Dunn is one of eight players to record five straight 40-homer seasons. He sought advice from one of the others, Ken Griffey Jr.

“He said (The Cell) was a great hitter’s park,” Dunn said.

As for the trade of Linebrink, at least Sox fans will be happy. He was a favorite of the boo-birds while posting ERAs of 4.66 and 4.40 the last two seasons.

Cofield, 23, spent most of last season in Class AA, going 1-3 with a 4.39 ERA with half his appearances coming as a starter.

dvandyck@tribune.com

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