Schneider has one more season left on his contract and can become an unrestricted free agent after 2014-15.
"It's a discussion about if they want me to be the guy going forward," Schneider told the newspaper. "We have to figure out that part of it."
Schneider, 28, went 16-15-12 in 45 games this season, his first with the Devils, and was third in the NHL with a 1.97 goals-against average. He said he would like to play in at least 60 per season going forward.
He said his future is in no way tied to Martin Brodeur. The 42-year-old franchise icon and NHL all-time leader in games played, wins and shutouts will be an unrestricted free agent July 1. Brodeur played 39 games this season, going 19-14-6 with a 2.51 GAA.
"Not just him, per se, but anybody who they would want to bring in or call up … it's not directly centered around Marty," Schneider said. "We'll probably find out in a few weeks what is going to happen."
Brodeur on Friday told ESPN.com he will test the market in an attempt to play elsewhere.
"I've had a lot of good conversations with the Devils, but I'm not inclined at going back at this point," Brodeur told Pierre LeBrun. "I just feel that with [Schneider] the organization has to move on. Me being around might be tough a little bit for them. I don't completely put [returning to New Jersey] out of the question, but I don't want to mess up the cards for the Devils."
Schneider had no other details pertaining to his talks with the Devils.
"We've spoken a little bit. We had the usual talks at the end of the season," he said. "[General manager Lou] Lamoriello said I'd be a priority. It would be very un-Devil-like of me to discuss any negotiations, but both sides have talked and we've made it known what we'd like to do going forward.
"It's early June so there is still plenty of time to continue talking. Right now there is nothing imminent to report. We've spoken a little bit."