Sources told Jeff Passan on Thursday that Elvis Andrus is going to sign with the White Socks.
The Oakland A's released Andrus on Wednesday, and he is expected to join the White Bulls in Cleveland on Friday.
Infielder/outfielder LeuryGarcia was placed on the 10-day injured list because of a strained lower back. In Anderson's absence, Garcia and Sosa had been splitting time at the position.
Andrus is hitting.237 with eight home runs and 30 runs scored. After 12 seasons with the Rangers, he was traded to Oakland.
The two-time American League All-Star has a career batting average of.270 with 87 homers and 701 runs scored.
Two games back in the American League Central and in the race for the final wild-card spot, the WhiteSox enter Thursday.