The Mariners declined to confirm Montoyo's interview, but the 50-year-old is known to be on Dipoto's list of candidates.
Dipoto has also interviewed Phil Nevin, who managed the D-backs' Triple-A Reno club last season, and is interested in two former Angels connections, Tim Bogar and Scott Servais.
While other candidates likely will emerge, those are the established names at this point in what has been a quiet process by the new GM, who was hired last month to replace Jack Zduriencik.
Montoyo, a native of Puerto Rico, has been in the Rays organization the past 19 years, with this past season his first on the Major League coaching staff. He managed at every level in the Rays' system over the previous 18 seasons, including the last eight years as the skipper at Triple-A Durham, where he led the Bulls to six International League finals and two Governors' Cup championships.
His career record at Durham was 633-515 and he holds the franchise record for wins, while also earning International League Manager of the Year honors in 2010 and '13, Baseball America Triple-A Manager of the Year in 2007 and Baseball American Minor League Manager of the Year in 2009.
Montoyo played 10 years as a Minor League infielder with the Brewers, Expos and Phillies organizations and reached the Majors for 27 days with Montreal in 1993.
Bogar and Servais both worked with Dipoto at Anaheim last year. Bogar, who went 14-8 as the Rangers' interim manager at the end of 2014, was hired by Dipoto as a special assistant to the GM this past season. The two were teammates with the Mets in 1995-96.
Servais has been with the Angels the past four years as assistant general manager overseeing scouting and player development. A former Major League catcher, he was a teammate of Dipoto with the Rockies in 2000 and also worked as a scout with the Rockies in 2005 when Dipoto was Colorado's player personnel director.
Servais has spent most of his post-playing career in the front office, heading the Rangers' player development department for six years before moving to Anaheim, and he recently interviewed for the vacant Padres managerial position.
Servais, 48, could also be a fit as the Mariners' player development director as Chris Gwynn resigned from that post in Seattle last week after four years as farm director.
Nevin, a 12-year Major League veteran and 2001 All-Star, has interviewed with the Nationals, Marlins and Padres as well as the Mariners over the past two weeks, according to the Orange County Register. The 44-year-old has been the manager at Reno the past two years.