The NFL has proposed increasing its COVID-19 testing cadence for vaccinated players as cases surge around the country and multiple teams deal with case clusters that have sidelined prominent players and coaches this summer.

The league wants to move testing for vaccinated players to once every seven days from once every 14 days, NFL general counsel Larry Ferazani said Thursday in a media briefing. Players who are not fully vaccinated would continue to be tested daily. The proposal requires approval from the NFL Players Association, which has been pushing for all players -- vaccinated and unvaccinated -- to be tested daily.

"That is based on our best effort ... to render the safest possible environment for our players," Ferazani said.

In a statement to ESPN, the NFLPA stopped short of accepting the proposal: "The COVID environment is constantly changing and our success last year was built not only on a foundation of cooperation, but more importantly, on listening to our experts. It is clear with what we know about the Delta variant and with what we have seen already with clubs, testing needs to be a greater focal point."

As of Thursday, nearly 93% of NFL players are at least partially vaccinated, according to NFL chief medical officer Dr. Allen Sills. Staff members have been nearly 100% vaccinated since the start of training camp.

Between Aug. 1 and Aug. 21, the league recorded 68 positive tests among all players and staff from 7,190 tests. Approximately seven times as many unvaccinated players have tested positive as have vaccinated players, per league data. Some teams have produced multiple positive tests at approximately the same time, most notably the Tennessee Titans, who are currently without coach Mike Vrabel and quarterback Ryan Tannehill, among others. But Sills said none of those instances have been classified as "outbreaks" because there was no evidence of "ongoing spread within the club on a widespread basis."

In one such cluster, which Sills declined to identify, 38% of a team's unvaccinated players were infected. One argument for increasing testing among vaccinated players is if they are found to be spreading the virus to teammates or even family members. Asked if that has happened and prompted the proposal for more tests, Sills said: "It's a complicated question to answer." He acknowledged that the league has seen "small clusters of positive cases among vaccinated individuals who share common exposure," but said it hasn't been clear who from that cluster had spread it to whom.

The NFLPA's push to test all players daily is rooted in protocols adopted for the 2020 season, which were put in place and carried out before vaccines were available. Sills, however, said that testing itself did not prevent outbreaks last season and that other mitigation policies -- including masking and avoiding in-person meetings and meals -- proved more valuable.

"People tend to focus on safety, and it's very important that we realize that testing is not prevention," Sills said. "Testing is not preventing anyone from transmitting the virus. It is one part of our mitigation strategy but it's not the key part. ... Testing is obviously something that is helpful and it can be beneficial but we try to apply it in a targeted and intelligent manner and we try to test those people that are most at risk, and that's what we'll continue to recommend. But it's not testing that will get us through this surge or the future of our season here."

ESPN's Dan Graziano contributed to this report.