In a conversation with Newsday on Monday, Lundqvist said, "There's more to just money in this," adding he's just as concerned with who the team puts around him.
"I love it here, I really do," Lundqvist said. "There's a few things we have to discuss, but like I keep telling everyone, I've had such a great time in New York with the way the fans have treated me and with the challenge to be here, I just love that part. We'll see what happens, but it will be fun to stay."
The 2013-14 season will be the final one in Lundqvist's six-year, $41.25 million contract. He can become an unrestricted free agent next July.
"Henrik wants to be here and we want Henrik," Rangers assistant general manager Jeff Gorton told reporters earlier this month. "At the end of the day, it shouldn't be too difficult to get a deal."
In eight seasons with the Rangers, Lundqvist has emerged as one of the top goalies in the NHL. His 276 wins are second on the teams all-time list, 25 behind Mike Richter, and his 45 shutouts are second to Ed Giacomin.
Lundqvist won at least 30 games in each of his first seven seasons, and won 24 in 43 games last season. He had a 2.05 goals-against average and a .926 save percentage, and was a Vezina Trophy finalist for the fifth time.
Lundqvist said he was ready to put last season behind him, including a second-round loss in the Stanley Cup Playoffs against the Boston Bruins. In addition, coach John Tortorella was fired and replaced by Alain Vigneault.
"As a group, it's always enthusing to see what a new coach can do," Lundqvist said. "But for me as a goalie, it doesn't really change; I approach the game the same way. With the guys we have right now, I think we are in the right direction and I'm anxious to get back on the ice."
Whether he has a new contract before training camp opens Sept. 11, however, isn't really an issue for him, he said.
"We're talking," Lundqvist said. "The good thing, though, is that we have another year, so there's no pressure to get it done. But we're definitely talking, and we'll see where it leads. So far it's been a great time in New York and I don't see any reasons to leave."