The Mets' managerial search appears to be down to four.
Martino reported Monday that the Mets were beginning a third round of interviews this week as they look to replace Mickey Callaway, who was fired after the season.
Bogar, 52, is a three-time Manager of the Year in the minor leagues and has worked on the big-league staffs of the Rays, Red Sox, Rangers, Mariners and Nationals.
He played nine years in the majors from 1993-2001 as an infielder with the Mets, Astros and Dodgers.
Perez, 50, enjoyed a 13-year major league career with the Angels, Reds, Cardinals, Devil Rays, Indians and Mariners.
Perez has managed the Puerto Rican and Colombian national teams. He was a hitting coach for the Marlins from 2011-2012 and bench coach for the Astros in 2013.
USA Today reported last week that Perez is seen as as the "clear front runner." SNY reported that both Perez and Bogar "have hit it off" with Mets general manager Brodie Van Wagenen.
With his sights set on the Mets opening, Beltran said he turned down opportunities to interview with the Cubs and Padres this year.
Shelton, 49, has spent the past two seasons as the Twins' bench coach -- this year Minnesota won the American League Central before being swept in their AL Division Series against the Yankees.
Shelton's background also includes serving as the hitting coach for the Indians and Rays and quality control coach for the Blue Jays. A former Yankees farmhand, he was a manager in the Yankees' minor league system for three seasons from 2000-02.
Other known candidates to have interviewed with the Mets are Diamondbacks Vice President of Player Development Mike Bell, Padres first-base coach Skip Schumaker, Brewers bench coach Pat Murphy and former Yankees manager Joe Girardi, who was hired last week as the Philadelphia Phillies' skipper.
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