The Pittsburgh Tribune-Review and Post-Gazette both reported Sunday the team likely will introduce Russell at a Monday news conference.
The 46-year-old Russell was the Pirates' third-base coach and catching instructor under former manager Lloyd McClendon from 2003-2005, and has never been a major league manager.
He managed the Triple-A Ottawa Lynx to a 55-88 record last season, and played for the Phillies, Braves and Rangers from 1984-93.
MLB.com reported Russell's hiring will end a near monthlong search by General Manager Neal Huntington -- who reportedly interviewed White Sox bench coach Joey Cora, Triple-A Indianapolis manager Trent Jewett, Cleveland third base coach Joel Skinner and Dodgers bench coach Dave Jauss.
Boston pitching coach John Farrell also was among those thought to be on the club's list of managing prospects.