Norrie is set to be seeded eighth at Flushing Meadows due to the absence of Novak Djokovic, who will miss out on the final major of 2022 owing to United States rules restricting non-citizens from entering the country without being fully vaccinated against coronavirus.
World number two Alexander Zverev has already pulled out with an ankle injury while Rafael Nadal has only played once since his retirement from Wimbledon, which could open the door for Norrie to back up his last-four showing at SW19 last month.
Murray said: "It's definitely more open this year but I'd imagine some of the guys that you would expect to go deep will go deep like your (Daniil) Medvedevs.
"I'd still expect Rafa to have a good tournament, (Carlos) Alcaraz and (Stefanos) Tsitsipas, but I do think there is going to be an opportunity there for Cam.
"Cam's ranked in the top eight if Novak doesn't play, right? So, that helps and it does matter. It doesn't guarantee making the job easier but it increases the chances because if a guy ranked 15 or 16 loses then you maybe don't play anyone in the top 25 before the quarter-finals.
"He's been very consistent against guys ranked below him for most parts of this year so he's definitely got the chance of a good run."
Murray and Norrie faced each other at the Western and Southern Open last week, with the latter winning 3-6 6-3 6-4.
World number 49 Murray, who won his maiden grand slam title at Flushing Meadows a decade ago, struggled with cramp during their two-hour-and-38-minute battle.
It was not the first time the 35-year-old had been hampered by the issue, which also impacted him against Mikael Ymer and Stan Wawrinka earlier this month.
"We are trying to understand exactly why it is happening because no one knows exactly why people get cramps," Murray, who underwent sweat-testing on Wednesday, explained.
"Some people do think it could be hydration-related, conditioning-related, stress-related or whether you have not eaten the right stuff. There could be a number of factors that go into it. It could be an underlying illness that is there and we're just trying to get some answers.
"Physically I feel pretty good in terms of (no) discomfort or pain but I've been having the cramping these last few weeks so that has been frustrating."
While Murray suffered an early exit in Cincinnati, he enjoyed watching Emma Raducanu find form in the women's tournament with impressive wins over Serena Williams and Victoria Azarenka.
Raducanu has - understandably - struggled for consistency since her incredible US Open success last September but the 19-year-old has produced some of her best tennis in recent weeks ahead of her title defence.
Murray added: "With Emma, I think she played really well last week. I watched a couple of her matches. I saw most of the match against Serena and then the one against (Jessica) Pegula and even though she lost that one, she is playing much better.
"The balls they use over here help a lot. They are a lot lighter, the women's ball, so that allows her to get more on her shots, on her serves and she seems like she enjoyed the conditions last week.
"I'd imagine it with it being quick here in New York she will enjoy the conditions and I'd expect her to play well."
While the British focus at Flushing Meadows will be on Murray, Norrie and Raducanu, the eyes of the world will all be on global superstar Williams, who confirmed earlier this month she was "evolving" away from tennis.
The US Open is expected to be the 23-time grand slam champion's final tournament and despite fairy tales being synonymous with New York, Murray says next week should all be about celebrating Williams' extraordinary career.
"Her and Venus have had a massive impact on the sport. They had Oscar-winning movies made about their careers," Murray added, referencing Will Smith's win as best actor for his portrayal of their father Richard in King Richard.
"Serena is much bigger than tennis. She is a proper global sports superstar pretty much everywhere she goes and I think she will go down as the greatest female player of all time.
"She has hardly played the last few years, so expectations on her run should be very low but the celebrations of her career should be really, really high. She will probably want this week to be about everything she has achieved, having a really nice send-off and it being more of a celebration rather than being really upset that it is the end."