Maddux is currently the pitching coach for the Rangers and helped guide Texas to World Series appearances the past two years. Maddux pitched 472 games in the Majors, 59 of them for the Red Sox between 1995-96.
His brother, Greg, was a 355-game winner in the Majors.
The Cubs, whose front office is run by former Red Sox general manager Theo Epstein, will also interview Maddux next week.
"Unbelievable to hear those two teams have interest," Maddux said as part of a series of responses he e-mailed to media members in Texas. "Both storied franchises, full of tradition, synonymous with history. The ballparks are shrines, and they have great fans year after year.
"I'm humbled to find how highly some other organizations feel about me. It's come upon our family and me quickly. Just last week we were in the World Series and managing another club was not in the gameplan."
The Rangers don't want to stand in the way of Maddux's career growth.
"Mike is in a key role for us and has had a prominent hand in our success the past few years," Rangers general manager Jon Daniels said on Thursday. "But this is a unique opportunity to discuss a coveted position with two storied franchises, and we believe in allowing our people to pursue opportunities that they're interested in. It reflects well both on Mike and our organization that he's under consideration."
Earlier this week, the Sox interviewed Phillies bench coach Pete Mackanin and Brewers hitting coach Dale Sveum.
While Maddux has extensive experience as a pitching coach in both the Major and Minor Leagues, he has never managed.
"Pitching and defense are considered the foundation of a winning team," said Maddux. "The better you pitch and catch, the better chance you have of winning. With that being said, I guess being a pitching coach is a level away from managing."
Alomar also doesn't have managing experience, but he was promoted to bench coach by the Cleveland Indians after the 2011 season. Alomar served as Cleveland's first-base coach the past two seasons. He was the roving catching instructor for the Mets in 2008-09.
The White Sox had also expressed interest in Alomar as a manager before going with Robin Ventura instead.
A former Major League catcher, Alomar had a 20-year career, hitting .273 with 112 homers and 588 RBIs. The six-time All-Star was highly regarded for his leadership and his defense and isn't too far removed from a playing career that ended in 2007. His father Sandy Alomar also had a long career, and brother Roberto was inducted into the Hall of Fame last summer.
While it was once rare for pitching coaches to have success as managers, Bud Black and John Farrell have started to change that perception, much like Roger Craig did in the late 1980s.
"Buddy and John have opened the door for former pitchers to advance in the game up to the manager's seat," Maddux said. "Because of their success I feel that teams are more open to look into the idea of a former hurler leading a team."