Some of the more than 400 proposition bets for Super Bowl LI between the Philadelphia Eagles and the New England Patriots are displayed at the Race & Sports SuperBook at the Westgate Las Vegas Resort & Casino on January 26, 2018 in Las Vegas, Nevada.

"Betting on sports may become widely legal, but we cannot allow those who have lobbied the hardest for sports gambling to be the only ones controlling how it would be ushered into our businesses. The athletes must also have a seat at the table to ensure that players' rights and the integrity of our games are protected."

"Given the pending Supreme Court decision regarding the Professional and Amateur Sports Protection Act (PASPA) ... The time has come to address not just who profits from sports gambling, but also the costs. Our unions have been discussing the potential impact of legalized gambling on players' privacy and publicity rights, the integrity of our games and the volatility on our businesses," the Players Associations said in a joint statement.

With the legalization of sports betting across the U.S. looking more likely, players unions from major North American sports leagues want a seat at the table. The Players Associations for the MLB, NBA, NFL and NHL announced on Thursday they collectively plan to serve as a voice distinct from the interests of those working to legalize gambling on games but whose motivation is profit-based.

Protecting the integrity of the game and the regulation surrounding it has been a topic of debate and the players wanting say in the matter should not come as a surprise. Part of the debate from the sports leagues' point of view has been focused on how they get paid.

The NBA and MLB, which have been the most vocal leagues from early on in the debate, have proposed a 1 percent integrity fee to be paid to leagues from the total pool of bets, to help cover the costs they will incur from compliance efforts to avoid betting scandals involving players. New York State's Senate recently introduced legislation that would provide leagues with a 0.25 percent fee. Some gambling experts argue that the size of any integrity fee could influence whether legalized sports gambling is successful as a business model — too high a fee could keep most of the action with illegal bookmakers.

Potential scenarios involving players and match-fixing is a real concern. Dr. Laila Mintas of Sportradar, a company that works with the officials and players of several leagues to deter scandals, including the those in the NBA and NHL, believes it makes sense to have all parties in on the conversations.

"All relevant stakeholders, including player unions, need to have a seat at the table as we approach this potential landmark change in the sports betting landscape in the United States. Maintaining the integrity of sport must be a key cornerstone of the discussions," Mintas said.

The NBA has previously emphasized the need to protect the integrity of the game and the organization is open to its players union being involved in the process, as NBA spokesman Mike Bass tells CNBC.

"We welcome the involvement of our players in this process and believe there is an alignment of interests of everyone involved in professional sports to protect the integrity of our competitions," Bass said.

The NFL declined to comment on NFLPA's stance, but did offer a statement on the upcoming U.S. Supreme Court decision that could allow states the ability to allow sports betting. "Regardless of the outcome, we will maintain our relentless focus on protecting the integrity of the game and ensure there are no improper influences affecting how the game is played on the field. If there are changes, we will work with regulators, operators, the clubs, players and others to ensure that our fans and the game and the people who play, coach, and officiate it are protected," an NFL spokesman told CNBC.