According to Sports Illustrated's Jon Heyman, the Red Sox have requested permission from the Rangers to speak to their pitching coach about the vacant job in Boston.
The Red Sox will have competition, though, from Theo Epstein, as Heyman added that the Cubs have also requested to interview Maddux.
Maddux, 50, is the older brother of eight-time All-Star Greg Maddux and worked as Texas' pitching coach for three seasons. The Rangers have made consecutive appearances in the World Series, with the team finishing eighth in the American League in ERA in 2009, fourth in '10 and fifth in 2011. The pitching staff he inherited posted the worst team ERA in the AL in 2008.
Maddux was expected to be a candidate for the Boston job, left open by Terry Francona's departure.