NFL Players Association president Eric Winston agreed with DeMaurice Smith's recent comments that a work stoppage in 2021 is likely, given the current relationship between the union and the league.

But Winston took it a step further Monday in an interview with television station WCPO in Cincinnati, suggesting that players shouldn't care that a strike or lockout "might kill the goose that laid the golden egg."

"Honestly, I don't care, and I don't think the guys in this locker room care whether [the NFL] is going to be around in 20 years because none of us are going to be playing," Winston, an offensive tackle for the Bengals, told WCPO. "So if these guys [the owners] want to own for a long time, then they can own for a long time. But another work stoppage might kill the golden goose."

Smith, the union's executive director, said last week that "the likelihood of either a strike or a lockout is almost a virtual certainty."

Speaking at a fan forum hosted by the Detroit Lions, commissioner Roger Goodell said he hopes the two sides can come to an agreement before a work stoppage.

"I think projections of whether there's going to be a work stoppage are really not the point," Goodell said. "The point should be let's sit down and figure out our differences and get it solved and do what's right for our fans and the game and try to make this an even more popular game collectively. And that's what I hope will happen."

The NFL's current collective bargaining agreement, which is set to expire in 2021, was finalized after a 132-day lockout in 2011.

Winston, 33, said the union is preparing its players for another prolonged labor dispute, and he emphasized that the long-term health of the NFL is not a concern of his.

"I'm certainly not worried about it," he said. "I'm not going to be around that long. I don't care if even if there are rookies in here. They're not going to be playing that long. So if this thing dies out in 20 years, it dies out in 20 years. That's not really my concern, and I don't think it's any of these players' concern in here, either."

Smith, when asked about Winston's comments during an interview Tuesday with ESPN's Outside the Lines, said the veteran offensive lineman is "a person who understands the frame and business of football."

"The owners locked us out the last time," Smith said. "They took the decision to make sure that people didn't have a place to work. They cut off the insurance to our families. They wanted to force an 18-game schedule. What are you supposed to do? Fight back, right?"

Winston is a 12-year veteran and has been the NFLPA's president since March 2014. He acknowledged that there are "always going to be issues between labor and management" and said that a work stoppage will be the "inevitable outcome" unless serious progress is made in negotiations.

The NFLPA has clashed in recent years with the NFL over player discipline in such high-profile cases as Adrian Peterson's suspension for child abuse, Tom Brady's Deflategate suspension and Ezekiel Elliott's suspension for alleged domestic violence.

Goodell said he thinks that although neither side is getting exactly what it wants, the current labor deal works for both sides.

"We believe that we have a labor agreement that is working well for the players, is working well for the NFL and, I think, as a result, is working well for our fans," Goodell said. "We think we should continue that. Now, does that mean we think it's perfect? No. Does that mean the players think it's perfect? No. But this should be a basis for us to work together and get it solved."

Winston also was asked Monday why he thinks fans tend to side with ownership in labor disputes.

"My personal theory is [fans] think they have a stake in the team," he said. "I was as blindsided by it probably as anybody [in 2011]. ... They don't look at the issues the way we look at issues: wages, hours, working conditions and health and safety. You could talk about the same thing in a coal miners' union meeting as we do in our meetings.

"I think fans look at the team and say that that's their team. They have an ownership in that. That's why you always hear fans say, 'Oh, the salary cap,' and they think they're kinda the general managers. Obviously, fantasy football and things like that play into it."

Information from ESPN's Michael Rothstein was used in this report.