NEW YORK — San Francisco Giants World Series star Pablo Sandoval was among 12 free agents given $15.3 million qualifying offers Monday by their former teams.

Detroit made the offers to pitcher Max Scherzer and first baseman-designated hitter Victor Martinez, and Pittsburgh to left-hander Francisco Liriano and catcher Russell Martin.

Also receiving offers were shortstop Hanley Ramirez (Los Angeles Dodgers), outfielder Nelson Cruz (Baltimore), right-hander James Shields (Kansas City), closer David Robertson (New York Yankees), outfielder Melky Cabrera (Toronto), pitcher Ervin Santana (Atlanta) and outfielder Michael Cuddyer (Colorado).

An offer could be made only to a free agent who was with the team for the entire season.

If a player rejects a qualifying offer and signs a major league contract with another club before the June amateur draft, his former team would receive a draft pick as compensation at the end of the first round.

The approximately 135 free agents can start negotiating money with all teams starting Tuesday.

Three players who potentially could have become free agents stayed with their teams. Third baseman Aramis Ramirez exercised his half of a $14 million mutual option with Milwaukee; left-hander Tsuyoshi Wada agreed to a $4 million, one-year contract with the Chicago Cubs; and Tampa Bay exercised a $2.5 million option on right-hander Joel Peralta.

Cardinals

Bell promoted to bench coach: In St. Louis, the St. Louis Cardinals signed David Bell to a two-year contract as bench coach to replace Mike Aldrete, who left last week for the same role with Oakland.

The 42-year-old Bell was assistant hitting coach last year. He played in the majors for 12 years with six teams including the Cardinals.

Bell was a minor league manager in the Reds organization from 2009-12 and third base coach with the Cubs in 2013 before joining St. Louis last year.

Nationals

Miller named assistant general manager: In Washington, the Washington Nationals hired Bob Miller as vice president and assistant general manager.

The club announced the move Monday.

The 50-year-old Miller spent the past nine seasons with the Cincinnati Reds.

Tigers

Trammell hired as special assistant: In Detroit, Alan Trammell is returning to the Detroit Tigers as a special assistant to team president Dave Dombrowski.

Trammell, who played 20 years for the Tigers from 1977-96 and was the MVP of the 1984 World Series win over San Diego, rejoins the franchise.

after spending the last four seasons as a bench coach for the Arizona Diamondbacks. Trammell was Detroit’s manager from 2003-05 and a hitting coach for the Tigers in 1999.

The 56-year-old Trammell will assist in on-field duties at both the major league and minor league levels. He’ll also be involved in all personnel meetings, travel throughout the minor league system and participate in community relations.

Dombrowski says Trammell is an outstanding baseball person who offers a wealth of experience and perspective.