ESPN reported that NHL commissioner Gary Bettman proposed to Donald Fehr, the NHLPA boss, a meeting between owners and players - without league or players association officials in the room.
Fehr and the players were apparently considering it.
Fehr did not address the issue when he released a statement, saying the mediators "informed the parties they did not think it was productive to continue the discussions further today." He added that the mediators would "stay in contact" and "call the parties back together when they thought the time was right."
This would be the second NHL season canceled in the last nine years.
Numerous issues are on the table, including how to divide hockey-related revenue - it reached a record $3.3 billion last season - free agency, arbitration, and length of contracts.
The NHL's latest offer was a 50/50 split of hockey revenue and $211 million in the "make whole" provision, which goes toward players' salaries. The players would agree to a 50/50 divide if it included $393 million.
But even if that issue is resolved, Daly said in an e-mail, the sides are far apart in many other areas.
With negotiations breaking down, speculation again surfaced about the NHLPA decertifying, a lengthy process that would enable the players to bring an antitrust suit against the NHL, claiming the lockout was illegal.
So far, the threat of decertification has not helped negotiations.
A board of governors meeting is set for Wednesday, during which more games could be canceled. As it stands, games have been canceled through Dec. 14.
Contact Sam Carchidi at firstname.lastname@example.org, or follow on Twitter @BroadStBull.