Sanchez has been out since suffering a Grade 1 strain of the brachialis muscle in his right arm during an at-bat April 8 at Baltimore.
In three rehab games with Triple-A Scranton/Wilkes-Barre this week, Sanchez was 5-for-13.
The Yankees open a three-game series Friday at Wrigley Field against the defending world champion Cubs.
Sanchez enjoyed a historic start to his big-league career last summer, hitting .299 with 20 homers and 42 RBIs in 53 games. He became the fastest player ever to hit 20 career home runs, doing it in 50 games.
Before his injury last month, Sanchez was off to a slow start, hitting .150 with one homer and two RBIs.
The Yankees, however, have managed to win without their young star, going 17-9 and leading the American League East.