Arnott, 38, had 17 goals and 17 assists in 72 games for the St. Louis Blues last season.
"I have no comment on it," Rangers coach John Tortorella said. "Nothing's been done yet. We've had discussion on a number of different players."
Arnott would provide much-needed forward depth for the Rangers, who have used defenseman Stu Bickel as a fourth-line forward and recently acquired Benn Ferriero, who will make his Rangers debut Saturday night against the Toronto Maple Leafs.
Arnott would bring a wealth of experience to the Rangers. In 1,244 career regular-season games, he has 417 goals and 938 points. In 122 Stanley Cup Playoff games, he has 32 goals and 73 points and won a Stanley Cup with the New Jersey Devils in 2000.