The Chicago White Sox have signed free-agent slugger Adam Dunn to a reported four-year, $56-million deal.

Joe Cowley, of the Chicago Sun-Times reports that the deal is done pending a physical that could happen as soon as tomorrow.

Last season Dunn had a .260 batting average, a .356 OBP and a .536 SLG, with 38 HRs and 103 RBI for the Washington Nationals. Dunn would primarily have to play DH.

The White Sox could still also bring back Paul Konerko, who is a free agent after turning down Chicago’s arbitration offer.

A person confirmed the deal to the Associated Press on condition of anonymity because the deal has not been officially announced. If Dunn passes a physical, he could be introduced Friday at a news conference.

Dunn hit 38 home runs with 103 RBIs for Washington last season. He hit .260 and is the big, left-handed bat the White Sox were seeking.

Even after adding Dunn, the White Sox are still hoping to re-sign Paul Konerko, who is a free agent after turning down Chicago’s arbitration offer.

The 31-year-old Dunn has a career batting average of .250, with 354 homers and 880 RBIs in 10 major league seasons with the Reds, Diamondbacks and Nationals. He is also prolific with strikeouts and had 199 last season, but would potentially put up big offensive numbers in homer-friendly U.S. Cellular Field.

The Nationals listened to trade offers for Dunn at the July deadline but decided not to make a deal. Reports say the White Sox were one of those teams interested at the time.

Dunn will give the White Sox the power lefty they have been missing since Jim Thome was shipped to the Dodgers at the end of the 2009 season. And when the White Sox decided not to reacquire Thome in 2010, he signed with the AL Central rival Twins.

During a conference call Thursday, White Sox general manager Ken Williams declined to directly address Dunn’s deal with Chicago, saying questions could be answered during a news conference Friday at 2 p.m. at the ballpark.

Williams said he definitely hopes to bring Konerko back and have his right-handed bat in the same lineup with Dunn. They would likely alternate at first and DH.

“Not only is there room for it, it would be the ideal fit from our perspective,” Williams said. “We can’t get too far ahead of ourselves.”

Williams said he’s trying to be patient and respect Konerko’s right to explore the free agent market. Konerko finished fifth in the AL MVP balloting last season when he batted .312 with 39 homers and 111 RBIs.

Williams said he presented two scenarios to owner Jerry Reinsdorf for approaching the season – one to go with younger players and move out veterans and the second to add to the current mix.

It’s obvious, that with the acquisition of Dunn, they went with the latter.

“We just didn’t want to be in the middle,” Williams said. “So the decision was if we’re going all in, we’re going all in. It’s been a difficult challenge to find the revenue to support the payroll and we’re out there on a limb a little bit obviously, but we think it is important we continue to try to add a few more significant pieces to the mix.”

It was a busy day for the White Sox. They declined to tender a contract to closer Bobby Jenks, who is second in club history with 173 saves. Jenks missed the final 27 games last season with ulnar neuritis in his right forearm.

Williams said he hasn’t closed the door on bringing back Jenks at a lesser salary. He made $7.5 million last year. Williams said he’d also had conversations with free agent catcher A.J. Pierzynski, who was not offered arbitration by the White Sox.

“I got to be careful at this point,” Williams said. “I’ll be completely honest, the next thing I would really like to put on the table or put back in uniform is Paul Konerko.”

Earlier Thursday the White Sox exercised a club option on shortstop Alexei Ramirez. He will earn a base salary of $2.75 million. He had opted out of the final year of the deal he signed on Jan. 22, 2008.

The Associated Press contributed to this report.

Watch & Listen LIVE