Here's a look at some teams that might come calling for his services at the trade deadline in March if the Devils don't think they can re-sign him, with some being more likely destinations than others.
The Kings could use another scorer in support of goaltender Jon Quick, and just imagine Parise paired up front with Anze Kopitar.
The Devils could ask for defenseman Jack Johnson in return. His plus-minus hasn't been anything to write home about, but he has great offensive upside and would also bring a physical presence.
A more likely return would be goaltender Jonathan Bernier, who is Quick's backup, but is also NHL-tested.
The Canucks could simply swap Parise for backup goaltender Cory Schneider, who will also be an unrestricted free agent next year, assuming Vancouver is willing to let Schneider go with starter Roberto Luongo being a hit or miss come playoff time.
The former Atlanta Thrashers franchise could use another marquee name in its second season in Manitoba, especially a bona fide scorer like Parise. He would be a great addition to a young cast of Jets forwards with a large upside, led by captain Andrew Ladd.
The Rangers have shown a willingness to throw money around in the past, and snagging Parise from their cross-river rival would be a coup.
But don't expect the Devils to trade him to New York, where he could definitely hurt them come playoff time. It's not like they'd get Brad Richards for him, anyway.
New Jersey might be willing to deal Parise to the Hurricanes for Eric Staal, who is off to a poor start so far this season (four goals and 10 points in 24 games) and might be in need of a change of address.
The highly-talented Staal also killed the Devils with his late game-winning goal in Game 7 in the first round of the 2009 playoffs, How ironic would it be to bring him to Newark, N.J., just three years later?
The Red Wings always seem to come up with great players, although that's usually through their own drafting or free-agent signings. But Parise would definitely give them another weapon in their lineup alongside Pavel Datsyuk and Henrik Zetterberg.
The Devils could try to get Jarome Iginla, if he wanted out of Calgary (which he doesn't seem to). But he's older now and has some wear and tear on him, and Parise probably has more upside than Iginla at this point.
At age 27, Parise might be almost a greybeard among the Oilers' young guns like Taylor Hall and Ryan Nugent-Hopkins, but he might hasten their development even further by adding a scorer like himself to their roster.
New Jersey could get an experienced player like Shawn Horcoff and/or Tom Gilbert in the deal, but there's no way Edmonton would give up its top two fledgling forwards in Hall and Nugent-Hopkins.
Could Parise be the X-factor that finally gets the Sharks to the Stanley Cup Finals? His work ethic and scoring touch would only complement the lineup, and could take some pressure off Joe Thornton and Patrick Marleau.
An equitable trade might include Ryan Clowe, who could provide the Devils with both scoring and literal punch up front. Joe Pavelski might be another possibility.