The 43-year-old Varitek, who retired in 2011 after playing 15 seasons with the Red Sox, has talked with new Mariners general manager Jerry Dipoto about the opening, the Boston Globe reported.
Tim Bogar, Alex Cora, Phil Nevin, Bud Black, Omar Vizquel and Charlie Montoyo have been linked to the Mariners' managerial opening. Seattle is not likely to make a decision until after the World Series, according to multiple reports.
The Mariners fired Lloyd McClendon on Oct. 9 after finishing the 2015 season in fourth place in the AL West with a 76-86 record.
Varitek had been serving as a special assistant to former Red Sox general manager Ben Cherington.
Varitek, a first-round pick by Seattle in the 1994 draft, spent three seasons in the Mariners' farm system and was traded to the Red Sox in 1997. The three-time All-Star selection went on to hit 193 home runs and had a .256 batting average with the Red Sox, with whom he won two World Series titles.