The former Dallas Stars teammates will be among the players considered when the Hall's 18-member selection committee sits down together Tuesday to determine the next group of inductees.
Hitchcock coached Nieuwendyk and Belfour in Dallas and believes they played key roles in the franchise's Stanley Cup win in 1999. Dallas was also a Cup finalist in 2000.
"Those guys are similar characters in that they both were prime-time players when it meant the most," Hitchcock said Monday from Columbus. "Especially Nieuwy, Nieuwy was a great player in big games and he was a great player in the playoffs.
"Eddie came to Dallas and he got in a competitive zone and he stayed in that zone for four years. You just knew if you had a lead halfway through the game he wasn't going to give up a goal."
Nieuwendyk owns arguably the best credentials of any player under consideration. Passed over in his first year of eligibility last June, the current Stars general manager won three Stanley Cups and an Olympic gold medal while amassing more than 550 goals and 1,100 points.
Belfour was a two-time winner of the Vezina Trophy and sits third all-time with 484 victories. He is in his first year of eligibility.
"We were the right team for the right city at the right time," said Hitchcock. "The players really helped sell the game in Texas, we had the right mix of young and veteran players, and we had tremendous leadership, which to me was the best quality.
"We had a team-first mentality and nobody allowed anyone to get in the way of that."
Others players who have previously been passed over in Hall voting that still merit consideration include Doug Gilmour, Pavel Bure, Kevin Lowe, Steve Larmer, Eric Lindros, Alexander Mogilny, Dave Andreychuk, Kevin Lowe and Bernie Nicholls, among others.
The Hall can only welcome four players each year and is coming out of a period that saw a high number of first-ballot inductees. Hitchcock would like to see Gilmour given a spot when the induction ceremony is held in November.
"I've always wondered why Doug Gilmour's not there," said Hitchcock. "Having coached against Doug Gilmour and knowing how he could just win games by himself, I've always found that surprising that he's never got into the Hall of Fame.
"I've really wondered about that."
Like many in the hockey world, he would also like to see Pat Burns included in the 2011 class. There was a strong public push a year ago for the three-time Jack Adams Award winner, who ended up dying of cancer at age 58 in November.
Other potential names that could be considered in the builder category include longtime Soviet coach Viktor Tikhonov and Gordon (Red) Berenson, who followed a successful playing career by helping turn the University of Michigan's hockey program into a powerhouse.
The Hall might also add members to the special women's category it established last year. Canadian defenceman Geraldine Heaney is considered a strong bet to find her way there.
A number of people will be anxiously waiting for the selection committee's decision on Tuesday afternoon. That includes Hitchcock, who will be pulling hard for Nieuwendyk and Belfour.
"I think they both deserve it based on longevity and performance under pressure," he said. "They're winners. They won Cups and I don't think you can dismiss that."