"I'm sure we'll figure something out as a team. I'm not sure exactly what that will be, but I'm sure guys will peacefully protest in some type of form or fashion," White told reporters during a video conference.
White was among 17 Patriots players who kneeled during the national anthem for one game in September 2017 in support of former NFL quarterback Colin Kaepernick. All Patriots players stood on the sideline and locked arms during the national anthem for the remainder of the season.
White, who has served as a captain the past two years, said the decision to kneel at the time was "difficult" but that "we wanted to stand with Kap. Being black people in America, we understood exactly what he was talking about."
In 2016, his final season with the San Francisco 49ers, Kaepernick kneeled during the pregame national anthem to protest racial inequality and police brutality.
White said Thursday that with more people now speaking out after George Floyd's death, things feel different to him than in 2017.
"I think people's awareness wasn't as heightened back then," he said.
Floyd, who was black, died May 25 in Minneapolis after Derek Chauvin, a white police officer, kneeled on his neck for more than eight minutes.
"Back in , it was clear as day that they weren't on board with anything Kap was trying to say and it was more about, 'Hey, how do we get guys to stand up for the national anthem? How do we get guys to not have fans booing us? How do we get guys to stand up so we don't lose sponsors?' It was all from a business standpoint," he said in the most recent edition of his "Double Coverage" podcast.
"I think everything that has gone on since then will push the envelope. Only time will tell what their actionable reaction will be, as opposed to just words. I think what's going to be special is that there are going to be a lot of players that are willing to do things and change those words into action."
The Patriots, like other NFL teams, talked about Floyd's death during their video conferences. Rahsaan Hall, the director of the racial justice program at the Massachusetts American Civil Liberties Union, was part of one discussion.
"It was cool to speak with him," White said, noting Devin McCourty's prior connection with Hall. "You educate yourself so the world has a better understanding, so that can we make change in a positive light. It's not going to change in one day.
"I think everybody is trying to speak out a little bit more, a lot more people being more comfortable letting everybody know how they feel. I think that's important because some people might not understand that racism and things of that nature still exist, but it does. The color of your skin unfortunately comes with different things in America.
"So just trying to raise people's awareness, trying to make changes. It's sad that things like that the George Floyd situation have been going on for year after year and time after time. People have to be held accountable for things like that. Some laws need to be changed. It all starts with a conversation. All these people speaking up is only going to help."