NBC broadcaster Dan Hicks confirmed that the network reached out to Woods during a conference call Wednesday with fellow broadcasters and producer Tommy Roy.
"We were all thinking how good that would be, who better, if he couldn't be there to play it, to voice it and have him a part of the show, but we were rebuffed," Hicks told reporters. "He didn't want to do it, and I totally understand his situation.
"There is a lot going on in his world right now, and there's also a part of Tiger that doesn't want to become this -- I don't want to, for lack of a better word -- a sideshow at an event where we should be concentrating on what's happening."
Woods continues to recover from the serious leg injuries he sustained in a car accident on Feb. 23 in a Los Angeles suburb.
The 2021 U.S. Open runs June 17-20 at Torrey Pines Golf Course. Woods, 45, is a three-time U.S. Open champion.
His last major victory came at the 2019 Masters Tournament. He finished tied for 38th in his last official tournament, the 2020 Masters in November in Augusta, Ga.
"I really believe that if [Woods] said yes to something, it would just be a non-stop parade of asks, and he would have to just, you know, start telling everybody no," Hicks told reporters.
"It would have been fantastic to have Tiger a part of it in that sense, but I understand that what's going on in his world that he wanted to kind of keep it low key and stay out of the limelight for this one and just hopefully he'll enjoy it at home watching it on TV and be inspired when we talk about what he did 13 years ago, and that's the best we can hope for."