Vizquel, 42, would give the White Sox a versatile backup for nearly all the infield positions. Last season, Vizquel played third base, second base and shortstop while batting .266 in 62 games for the Rangers.
The White Sox said Friday that beside the five additions the club made to its 40-man roster, there would be no other news.
In addition to the 11-time Gold Glove winner providing solid defense, Vizquel would also give the White Sox a veteran infielder to help mentor shortstop Alexei Ramirez and second baseman Gordon Beckham, who is making his second position change in two years.
This is not the first time that the White Sox have had interest in Vizquel. The club was close to signing him to a two-year deal before the start of the 2005 season, but Vizquel instead inked a three-year contract with the Giants at the last minute.
Should the White Sox complete a deal with Vizquel, it could pose a serious challenge for Jayson Nix and Brent Lillibridge. Barring any other additions, the two players could be competing for one roster spot.
The White Sox selected the contracts of outfielder Stefan Gartrell and right-handed pitchers Brandon Hynick, Santo Luis, Brian Omogrosso and Sergio Santos to finalize their 40-man roster in advance of next month's Rule 5 Draft.
Kelly Thesier is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.