General manager Joe Garagiola Jr. said interviews are scheduled for three others, and he expects to talk with two more.
Manny Acta, third base coach for the Montreal Expos, will be interviewed on Tuesday; Wally Backman, manager for Arizona's Class A team in Lancaster, Calif., on Wednesday; and Jamie Quirk, bench coach of the Colorado Rockies, on Thursday.
Garagiola said he had not scheduled interviews with either of them but hoped to do so soon. He said he had yet to talk to Maddon to measure his interest in the Arizona job.
"I'm hopeful that by the end of the week we will feel we've got a group that we can make some recommendations to ownership on," Garagiola said.
Melvin served as manager Bob Brenly's bench coach in 2000 and in the World Series championship season of 2001 before leaving to replace Lou Piniella as manager of the Seattle Mariners.
The Mariners went 93-69 in 2002 but faded to 63-99 this year, and Melvin was fired the day after the season ended.
"We were interested in asking him about his experiences as manager, and what were the positives that he took from that," Garagiola said. "It was another good session."
Grace, who retired as a player after the 2003 season and was a television analyst for Arizona games this year, has repeatedly expressed his desire to manage in the major leagues.
Brenly was the team's television analyst when he was hired to replace the fired Buck Showalter. But unlike Grace, Brenly had experience as a major-league coach.
Asked about Grace's inexperience as either a coach or manager, Garagiola said, "You can neither discount it, nor is it an automatic disqualifier. If it was a disqualifier, we wouldn't have interviewed him."
Pedrique, who began the year as Arizona's third base coach, took over as manager for the remainder of the season after Brenly was fired on July 2. The injury-ravaged Diamondbacks went on to lose 111 games, tied for eighth most in baseball history.
Backman has managed in the minors since 1997 after a 14-year major-league playing career, nine of them with the New York Mets.
In this his first season with Lancaster, he was named Sporting News manager of the year after leading the JetHawks to division titles in both halves of the California League season.
Backman has also been mentioned as a possible replacement for the fired Art Howe as manager of the Mets.
Acta has been a coach with the Expos for three seasons. He managed in the minors for eight years.
Quirk played 18 seasons in the big leagues before retiring in 1993. He held coaching positions with Kansas City and Texas and then joined manager Clint Hurdle, a former teammate, in Colorado in 2003.
Hale managed Class AAA Oklahoma for two seasons before becoming first base coach for the Rangers.
Maddon has spent 30 years in the Angels organization, the last 11 as a member of the big club's coaching staff. He lives in Mesa, Ariz.
Garagiola said the team began with a list of about 30 potential candidates.
Jeff Moorad, a prominent player agent, officially takes over as the Diamondbacks' chief executive officer on Friday.