McGwire, 52, who spent the last three seasons as the Dodgers' hitting coach, had his contract expire at the end of October. McGwire was hitting coach with the Cardinals for three seasons (2010-12) before joining the Dodgers.
McGwire, a native of Pomona, starred at USC before embarking on a 16-year big league career with the A's and the Cardinals. He hit 583 home runs, including 70 during the 1998 season.
To date, the Padres have yet to officially announce any hirings -- though pitching coach Darren Balsley and third-base coach Glenn Hoffman are returning.
This past week, Astros assistant hitting coach Alan Zinter was hired as the Padres' hitting coach, according to a source. Tarrik Brock will coach first base and former Padres pitcher Doug Bochtler will be the bullpen coach.
All that's left is the position of bench coach, one the Padres have mulled over since Green, a first-time big league manager, was hired last month.
"You always want to have guys who complement your [manager's] skill set. I don't look at it where it has to be someone who has to fit three or four experienced criteria, guys who have managed or coached before," said Padres general manager A.J. Preller last month.
Green spoke with potential candidates at the General Managers Meetings in Florida a week ago. Ron Gardenhire, one of three finalists for the Padres' manager job, was asked if he was interested in the position.
"In my mind, every single coach position should provide value to the team," Green said last month. "I would love experience for the bench coach position, but more than anything, someone who wants to push things forward for the organization."
Corey Brock is a reporter for MLB.com. Keep track of @FollowThePadres on Twitter and listen to his podcast. This story was not subject to the approval of Major League Baseball or its clubs.