Shesterkin and Alexandar Georgiev are the top two goalies on the depth chart in the Rangers' first training camp without former longtime No. 1 goalie Henrik Lundqvist since 2003.
New York bought out the final season on Lundqvist's contract following last season.
"In this season, every team in this league is going to have to rely on their two goalies," Quinn said Tuesday. "We're fortunate because we feel that we have two No. 1 goalies. I'm not just saying that. [Georgiev] has had a good career so far. I think he's ready to make the next step. [Shesterkin], in a small sample, certainly proved he can be a really good goalie at this level. We feel we have great goaltending depth and both of these guys are going to be contributors. We're certainly going to lean on both of them during the course of the season."
Shesterkin went 10-2-0 with a 2.52 goals-against average and .932 save percentage in 12 starts for the Rangers last season, his first in the NHL, after he was recalled from Hartford of the American Hockey League on Jan. 6. He started one game in the Stanley Cup Qualifiers, a 4-1 loss to the Carolina Hurricanes that eliminated the Rangers in Game 3 of the best-of-5 series Aug. 4.
Quinn said 13 games of NHL experience last season is enough for him to believe Shesterkin can be a top goalie in the NHL as soon as this season because of how good he was and that he's 25 years old with several seasons of professional hockey behind him.
"We have to keep in mind he's not a 22-year-old kid who came out of college or junior hockey," Quinn said. "He's got a pro background where he's had an awful lot of success."
Shesterkin, who turned 25 on Dec. 30, was one of the best goalies in the AHL prior to his recall after being arguably the best goalie in the Kontinental Hockey League from 2016-19. He said he has gotten quicker and better at positioning and reading the play since arriving in the NHL and working with Rangers goaltending coach Benoit Allaire.
"My expectations are to work even harder to increase the win column for the team, to increase all the goaltending statistics that are trackable and try to become the No. 1 goalie on this team," Shesterkin said.
Georgiev was 17-14-2 with a 3.04 GAA, .910 save percentage and two shutouts in 34 games (32 starts) last season. He is 35-31-7 with a 3.00 GAA and .913 save percentage in 77 games (71 starts) over three NHL seasons, all with New York.
The Rangers carried three goalies after recalling Shesterkin, and Georgiev was a healthy scratch for 11 of the final 29 games of the regular season.
Quinn said the second half of last season was difficult for Georgiev after he'd experienced some success, but the coach liked the way the goalie handled himself and New York has a lot of confidence in him.
"I think we have two really good goalies who will do whatever it takes to help the team win," Shesterkin said. "Obviously it would be quite an experience to be the face of the franchise, but so much has to be done to achieve that level of success. I began working very hard in an attempt to not disappoint myself and the fans before last season and take it very seriously, but much work has to be done to get there."
