Nash had 15 goals and 36 points in 60 regular-season games last season after scoring 42 goals (third in the NHL) with 69 points in 79 games in 2014-15.
"I don't think it was a very good season for myself, personally," Nash told the New York Daily News. "I'm looking at this as a fresh start and a chance to prove myself. We've got a lot of young talent here in camp and guys are fighting for a job. … I don't consider my job safe at all."
New York signed forwards Jimmy Vesey and Pavel Buchevnich this offseason and traded for forward Mika Zibanejad with plans to try them in the top six.
Nash has two years remaining on an eight-year, $62.4 million contract and is the highest paid Rangers forward making $7.8 million annually.
"But I know why I'm here and why I get paid to do what I do, and that's to score goals," Nash told the newspaper. "I've just got to be that much better and try harder to get more goals."
Despite his salary and NHL resume, Nash said he feels a roster spot won't just be given to him.
"It's the right attitude to have," Rangers coach Alain Vigneault said. "A player should want to come here and earn the ice time. In Rick's case, we talked about it [Thursday]. [He is a] solid two-way player but there's no going away from the fact that we need his offense. We need him to be on the scoresheet. We need him to be a force offensively.
"That offense that he brings, he's one of the elite offensive players in the game, and we need that from him."
Since entering the NHL in 2002-03, Nash ranks third with 393 goals behind Jarome Iginla (437) and Alex Ovechkin (525). In his second NHL season in 2003-04, with the Columbus Blue Jackets, Nash won the Rocket Richard Trophy with 41 goals.
A leg injury caused Nash to miss 22 games last season and it clearly affected his play, but the veteran said that shouldn't have held him back.
"It didn't really feel 100 percent until later in the summer, but it's no excuses," Nash said. "I don't think you can find one guy around the League that's playing at 100 percent. It's always tough coming back from an injury. It was a challenge, but everyone does it."
