The NHL has previously said that if a new labour agreement is not reached before the current one expires on September 15 it is prepared to lock out players rather than operate under the old deal while carrying on negotiations.
"Nobody on the players' side is talking about stopping the season. Nobody on the players' side is talking about having negotiations go up to a certain date and then that's all," NHL Players Association head Donald Fehr said.
"I have been in experiences before in which you play without a contract under the old rules and you continue negotiating and try and find a deal.
"We hope there isn't (a lockout), we don't think there is a reason for it. If they choose to do it you should understand it's something they chose to do."
A proposal submitted by the NHL last month showed a desire to have players give up a significant amount of salary to help stabilise the industry, but the union, who presented their offer on Tuesday, feel that would be best accomplished if the owners agreed to share greater revenue with struggling teams.
So while both sides have reached common ground on smaller issues, including player safety, there remains a significant gap with regards to the economics of a new labour agreement as many teams feel they cannot survive under the current system.
"The players made a proposal last week which we believed was designed to be both forthcoming and to allow us to bridge such gaps ... and essentially to partner with large income clubs and helping out any teams which may need it," said Fehr, who was in Chicago for regional player meetings.
"I still remain hopeful that that proposal will remain the basis for discussion as we go forward."
Formal discussion between the two sides are scheduled to resume on Wednesday in Toronto.
The NHL wants to reduce the players' share of hockey-related revenues to 46 per cent from 57 per cent despite enjoying record-breaking revenue of $3.3. billion last season, up from $2.2 billion before the 2004-05 lockout that wiped out a full season.
In a bid to slow the increase of salaries, the NHL's offer also calls for the elimination of salary arbitration, 10 years of service before unrestricted free agency kicks in (up from seven in the current deal) and limiting contracts to five years.
But the union wants to see the league commit to a system of revenue sharing that would require the NHL's wealthiest teams give over $250 million per season to struggling franchises.
The NHL's 82-game regular season is scheduled to start on October 11.