The league will also announce finalists for the Jack Adams Award (outstanding coach), Calder Memorial Trophy (outstanding rookie), James Norris Memorial Trophy (outstanding all-around defenceman), Frank J. Selke Trophy (outstanding defensive forward), Vezina Trophy (outstanding goaltender) and Lady Byng Memorial Trophy (sportsmanship and gentlemanly conduct).
Nominees for the NHLPA's Lester B. Pearson Award (most outstanding player as voted by players) will also be announced Tuesday.
The winners will be announced June 14 in Toronto.
Crosby and Luongo could be in the mix for both the Hart (NHL MVP) and Pearson Award. Other viable candidates include Martin Brodeur of the New Jersey Devils, Vincent Lecavalier of the Tampa Bay Lightning and Joe Thornton of the San Jose Sharks.
The 19-year-old Crosby became the youngest player in history to win the Art Ross Trophy as the NHL's top scorer with 120 points (36-84) in 79 games while also sporting a plus-10 rating.
"In addition to leading this team, there's the added pressure of being the go-to guy off the ice for the league," Pens GM Ray Shero told The Canadian Press last month. "But on the ice it doesn't affect him at all. It's hard not to say enough good things about the kid.
"He's a team-first player. He never takes a shift off. When your best player is your hardest-working player, it's great."
Luongo was second in the NHL with 47 wins as well as fourth in the league with a .921 save percentage and sixth with a 2.29 goals-against average, by the far the biggest reason in Vancouver's surprising season, playing 76 of his team's 82 games.
Brodeur has a strong case as well, topping the NHL with a record 48 wins while posting a 2.18 GAA and .922 save percentage while also registering a career-high 12 shutouts.
Thornton, last year's Hart and Art Ross winner, finished second in scoring with 114 points (22-92) in 82 games while Lecavalier was right behind at 108 points (52-56), leading the NHL in goals.
Evgeni Malkin of the Penguins and Paul Stastny of the Colorado Avalanche are the favourites for the Calder and that's not surprising given they finished 1-2 in NHL rookie scoring. Also worthy of consideration are Jordan Staal of the Penguins, Anze Kopitar of the Los Angeles Kings, and San Jose Sharks blue-liners Matt Carle and Marc-Edouard Vlasic.
The Norris could once again be a battle between the usual suspects, Nicklas Lidstrom of the Detroit Red Wings and the Anaheim Ducks dynamic duo of Scott Niedermayer and Chris Pronger although Dan Boyle of the Tampa Bay Lightning, Sergei Zubov of the Dallas Stars and Chris Phillips of the Ottawa Senators also merit consideration.
Lidstrom picked up his fourth Norris in five seasons last year.
The candidates are once again numerous for the Jack Adams. One can make a case for Alain Vigneault in Vancouver, Randy Carlyle in Anaheim, Mike Babcock in Detroit, Michel Therrien in Pittsburgh and reigning winner Lindy Ruff in Buffalo, among others.
Luongo and Brodeur will surely be finalists for the Vezina and should be joined by either Detroit's Dominik Hasek or Calgary's Miikka Kiprusoff, last year's winner.
The NHL's best defensive forward is a wide-open race this season. Jay Pandolfo of the Devils, Samuel Pahlsson of the Ducks, Henrik Zetterberg of the Wings and Mike Fisher of the Senators all merit consideration.