The offers to Konerko and Putz mean the White Sox will be compensated with draft picks should either player sign with another club.
Konerko finished fifth in the AL MVP balloting after batting .312 with 39 homers and 111 RBIs last season. Putz was 7-5 with a 2.83 ERA and three saves in 60 appearances.
Pierzynski batted .270 with nine homers and 56 RBIs. Ramirez, a late-season acquisition, batted .261 in 24 games with a homer and two RBIs.
Chicago can still negotiate with Pierzynski, regardless of whether arbitration was offered.
"In short, Paulie, A.J. and J.J., we remain interested in," general manager Kenny Williams said. "But obviously I have to let the market define their value and whether or not they are affordable to our club. This is part of the game that is a baseball offseason."
Williams suggested that not offering arbitration to Pierzynski was a sign of respect.
"We felt that if we did offer arbitration to A.J. and there were [compensation draft] picks involved that it would potentially hurt a guy that is loyal to us and has been a stud behind the plate and brings it every day," Williams said. "We just didn't want to do that. The market will define what his worth is and there will be a time in the offseason when we will get together with his guy and discern the options for bringing him back and whether it's affordable."
Asked whether or not the Konerko negotiations are progressing smoothly, Williams said he was looking toward the Dec. 5-9 MLB Winter Meetings.
"There is not much for us to talk about now," he said. "When you have guys the caliber of these guys, they have to have the time to go through the winter meetings to find out where they fit in the market place. Not until that time will we get a read on if it's something that fits in our payroll structure. To a large degree, we are in a holding pattern."
Doug Padilla covers the White Sox for ESPNChicago.com. Information from The Associated Press was used in this report.