The voting for the award was conducted among the league's 30 general managers, and the finalists were announced Friday.
The winner will be revealed at the NHL's awards banquet on June 24 in Las Vegas.
Varlamov earned a league-best 41 wins, breaking Avalanche coach Patrick Roy's club record for wins in a season. He was 7-1-1 when facing 40 or more shots.
Bishop won a Lightning-record 37 games and set a franchise mark with a .924 save percentage.
Rask had 36 wins and helped the Bruins capture their first Presidents' Trophy (team with the league's best regular-season record) since 1990. He finished first with seven shutouts and was second with a .930 save percentage.
"It's something that comes after the Stanley Cup," Rask said of the Vezina. "That's your main goal. If you get nominated, it's great. If not, then it doesn't matter. But I feel honored to be nominated and happy to go to Vegas for the first time in my life."
ESPNBoston.com's Joe McDonald contributed to this report.