May, who had two hits as the leadoff hitter Tuesday, will not bat leadoff immediately for the White Sox, Colleen Kane of the Chicago Tribune reports.

May has emerged as Chicago's starting center fielder after the team traded Peter Bourjos to the Rays on Monday. Manager Rick Renteria does not want to put the pressure of leading off on the rookie May, who has a career .273 batting average and .332 on-base percentage in the minors, though Renteria feels he could eventually become the leadoff guy. May spent 14 spring games as the team's leadoff hitter and another seven in the nine-hole.