They then might be told to switch to a less dangerous position - or give up football entirely.
"In talking to the medical experts over several years, I think there's a predisposition to most injuries, particularly to the brain, or to brain disease," Goodell said in an interview with The Associated Press on Monday. "So we do want to know what those biomarkers are."
Goodell also envisions players being required - with the union's OK, of course - to wear helmets containing sensors to detect hits that cause concussions. Those helmets might be lighter and "less of a weapon" than today's, he said.
Those are the kinds of advances the NFL and General Electric are hoping to produce in a partnership that could funnel up to $60 million over four years to research on head injuries and possible improvements to helmets.
"Imaging of the brain, studying the brain, is still pretty far behind the study of cancer, heart disease, things like that," GE Chairman and CEO Jeff Immelt said. "I look at this as a catalyst in terms of where the technology will go. ... I would say you're going to start seeing really strong activities almost immediately."
Goodell, who spoke to the AP after a news conference at a GE office building, agreed about the importance of quick progress.
"We weren't looking at a long timetable," he said. "We wanted to see results quickly."
Not long after Goodell was forced to defend the league's concussion policies at a congressional hearing in October 2009, the NFL began making changes. Among them: new return-to-play guidelines; changing the co-chairmen of the NFL's committee on concussions; and, expected for next season, putting independent neurological experts on sidelines during games.
Thousands of former players are suing the league and its teams, saying that for years the NFL did not do enough to protect players from concussions. Next month, a federal judge is scheduled to hear oral arguments on the league's motion to dismiss.
Such scrutiny "has no impact" on projects like the one with GE, Goodell said.
"This is about looking forward," he said. "This is about the future. This is about changing the way all of our lives are led, whether it's riding a bicycle or playing football or being a member of the military."
In September, the NFL announced a donation of $30 million for medical research to the Foundation for the National Institutes of Health, the NIH's fundraising arm.
One influential NFL owner, Robert Kraft of the New England Patriots, is pleased to see these kinds of projects now.
"I wish it had happened sooner. The evolution, the issue has been coming to the forefront and ... a lot of times we didn't talk about it, or talk about it enough. But we need to talk about it and do something about it," Kraft said.
"Everyone has been spending money in bits and pieces, but now it will be concentrated and this will become a tremendous resource," he added. "I don't think anyone has the answers, how to treat it, whether to continue to play - there haven't been answers, and we need to find the answers."
The Head Health Initiative described Monday, which also includes sports apparel and equipment maker Under Armour, involves a four-year, $40 million research and development program to find ways to detect and diagnose brain injuries, and a two-year "innovation challenge" that would put up to $20 million toward research to protect against those injuries.
Goodell thinks helmets can be improved.
"The better protection the helmet provides, sometimes the more likely (players) are to use their head, and that's a dilemma that we have to change, in part through rules," Goodell said. "But I also see that we could potentially change the helmet by making it lighter. (That) would make it less of a weapon."