Cabrera, 34, will replace Bobby Crosby as Oakland's starting shortstop. Cabrera hit .281 with eight home runs and 57 RBIs and stole 19 bases for the White Sox last year.
The Athletics said there would not be an announcement Monday. The deal is contingent on the 34-year-old Cabrera's passing a physical.
The Athletics have had substantial talks with Garciaparra in the past 48 hours, and the player's choices are between the A's and retirement, the sources said. Oakland also is negotiating with veteran reliever Dennys Reyes.
If Oakland were to sign Garciaparra, Crosby could be moved to a utility position. Cabrera is a two-time Gold Glove winner at shortstop, having won the award in both leagues (2001 with the Expos and 2007 with the Angels).
In 1,572 games, Cabrera is a career .274 hitter with 105 home runs and 684 RBIs.
Crosby, the 2004 AL Rookie of the Year, came to camp as the A's incumbent shortstop, but it was widely know the A's were looking elsewhere.
Crosby, who has a lifetime batting average of .239 and has missed considerable time to injury, spent six weeks during the offseason working with former major leaguer Mark McGwire.
"I want to get better," Crosby said recently. "I know I haven't played as well as I can. I'm changing my approach, my stance. For the most part I think there's always something I can improve upon. I know I have the support of the guys. I take the attitude I'll go out and play."
Crosby finished with an on-base percentage under .300 in each of the past three years. He has cut down on his strikeouts but he has also cut down on his walks, and he hits into too many double plays.
A's manager Bob Geren told the media earlier in the spring that Crosby "is going to be in the lineup and he's going to play."
Crosby hit a home run in his first spring at bat, a towering drive off Milwaukee's Manny Parra. He's hit safely in his first three starts and was batting .429 through Sunday.
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