The prospective deal between the NFL and its players’ union to modify the sport’s drug policies potentially could result in reduced or overturned suspensions for wide receivers Josh Gordon of the Cleveland Browns and Wes Welker of the Denver Broncos, according to two people familiar with the deliberations.

Both of those people, who spoke on the condition of anonymity because the negotiations between the league and the NFL Players Association remained at a sensitive stage, said the agreement likely would have to be completed before Sunday’s league-wide slate of games is played for modifications to the Gordon and Welker suspensions to be considered.

It also is not certain that the suspensions would be modified even if the comprehensive deal on the drug policies is completed, both people with knowledge of the talks said.

One of those people called it “possible” that the suspensions of Gordon and Welker could be affected by an agreement. According to that person, some on the players’ side are particularly eager for the NFL and the union to apply the finishing touches to the prospective deal, which would put blood-testing of players for human growth hormone into effect and also could result in other significant changes to the sport’s drug policies.

The other person confirmed that modifications to the Gordon and Welker suspensions were possibilities but not certainties if the drug-policies agreement is finalized.

George Atallah, the union’s assistant executive director of external affairs, said Thursday night: “We have been eager to get a fair and comprehensive deal on new drug policies done for three years. The manufactured hype does not bring us any closer.”

The potential effect on the Gordon and Welker suspensions was first reported by NBC and Profootballtalk.

Gordon has been suspended for the entire season for a violation of the NFL’s substance abuse policy. Welker was suspended for the first four games of the season for testing positive for a banned performance-enhancing substance.

It’s possible that neither player would have been suspended if some of the provisions currently being discussed by the league and union had been in effect at the time.

According to multiple people familiar with the discussions, one possible modification under negotiation is that the threshold for what would constitute a positive test for marijuana could be raised. Gordon’s suspension, according to reports, resulted from a positive test for marijuana in which one of the two urine samples taken from him was barely above the current threshold for a positive test and the other was below it.

Another potential change being discussed, according to those with knowledge of the deliberations, is that a positive test for amphetamines could be covered under the substance abuse policy rather than under the performance-enhancing drugs policy, and a positive test during the offseason would not necessarily result in a suspension. Welker reportedly tested positive for amphetamines during the offseason.

The comprehensive deal between the league and union, if completed, might increase penalties for drunk-driving incidents, according to those with knowledge of the talks, and it would put HGH blood-testing into effect. The NFL and NFLPA agreed as part of their 2011 labor deal that players would be tested for HGH. But the two sides first had to agree to the details of the testing program. That hasn’t happened yet, and testing has remained on hold for three entire seasons. HGH is on the sport’s list of banned performance-enhancing substances but players are not tested for it.

“Players who have been to any collective bargaining negotiation understand that we never describe them as ‘very close,’ ” Eric Winston, the veteran offensive lineman who is the president of the union, said in a written statement released earlier Thursday by the NFLPA. “We look at every issue we can to improve the rights and benefits of players. This process takes time, it takes creativity and it is never easy.

“We want to get a new agreement in place but we understand the responsibility we have to the players and to the game. It is critical that we get this right.”