The 32-year-old, who would get a $500,000 deal if added to the 40-man roster, had ligament replacement surgery in his left elbow last July, after hitting .237 with four home runs and 16 RBI in 41 games for Oakland. He didn't play after May 25 because of elbow problems and went on the disabled list for the seventh time in his career.
He joined the Rangers for their first full-squad workout Tuesday and took batting practice. He was to meet with manager Buck Showalter to discuss his role.
In 2004, Durazo was fifth in the AL with a .321 batting average while setting career highs with 164 hits, 36 doubles, 22 home runs and 88 RBI.
Over parts of seven major-league seasons with Arizona (1999-2002) and the Athletics (2003-05), Durazo has a .281 average with 94 home runs and 330 RBI in 624 games. Showalter was in Arizona for Durazo's first two seasons before the Diamondbacks won the World Series in 2001.
Durazo has a .338 average (27-for-80) with three homers and 13 RBI in 21 career games in Arlington.