Devils chairman/managing partner Jeff Vanderbeek, general manager Lou Lamoriello and Kovalchuk's agent, Jay Grossman, met with NHL executives at the league's New York office Monday.
NHL deputy commissioner Bill Daly, who confirmed the meeting about Kovalchuk's contract situation took place, said: "There was no new contract submitted. We talked conceptually."
Yahoo Sports, however, reported that terms for a new contract were presented to the NHL and that a decision from the league was expected within 24 hours.
The meeting is just the latest twist in Kovalchuk's strange free-agent summer.
On July 19, the Devils signed Kovalchuk to a 17-year, $102 million deal, but the league formally rejected the contract the following day. The NHLPA filed a grievance with the league July 26, forcing an arbitration hearing to decide the matter.
On Aug. 9, arbitrator Richard Bloch upheld the league's decision to void the deal, and Kovalchuk was returned to the free-agent market.
Since then, the Devils have continued their efforts to sign the star winger. Commissioner Gary Bettman said last week the league would be willing to advise teams on an acceptable structure for Kovalchuk's contract, but did not confirm if any team had approached the league.
E.J. Hradek is a senior writer at ESPN The Magazine. Information from ESPN.com's Scott Burnside was used in this report.