An official announcement is expected on Thursday, but no press conference will occur before Friday, the source said. Club officials have not confirmed the report.
It was first reported by CBSSports.com on Wednesday morning that Stewart would be offered Arizona's GM job.
Stewart, 57, has a diverse background in baseball, having been a successful Major League pitcher, then a pitching coach and an assistant GM. Most recently, he has worked as a player agent representing, among others, Dodgers outfielder Matt Kemp.
Given his longstanding relationship with chief baseball officer Tony La Russa, who managed him with Oakland, Stewart had been regarded as the front-runner since his name first surfaced as a candidate. La Russa has expressed in the past how impressed he has been with Stewart's background.
La Russa spoke with nine candidates in addition to Stewart, including Watson, Allard Baird, Larry Beinfest, Billy Eppler, Gary LaRocque, Thad Levine, Ray Montgomery, Hal Morris and Tim Purpura. Stewart won 168 games over a 16-year career, and he won at least 20 games in four consecutive seasons from 1987-90.
Stewart was a part of three World Series championships, with the Dodgers in 1981, the A's in '89 and the Blue Jays in '93.
Known as a big-game pitcher, Stewart was named the Most Valuable Player of the 1989 World Series and both the '90 and '93 American League Championship Series.
Prior to becoming an agent, Stewart worked in the Oakland A's front office as a special assistant to general manager Sandy Alderson in 1996, then was a special assistant to general manager Kevin Towers with the San Diego Padres in '97. He then went to the Blue Jays where he was assistant general manager from '98-2000 and had the added responsibility of overseeing both player development and scouting in '01. Stewart also held the position of pitching coach with the Padres ('98), Blue Jays ('00) and Milwaukee Brewers ('02) before leaving for the private sector.
Steve Gilbert is a reporter for MLB.com. Read his blog, Inside the D-backs, and follow him on Twitter @SteveGilbertMLB. This story was not subject to the approval of Major League Baseball or its clubs.