The number is well down on the record 10,127 who entered in 2014.
While only 54 players are currently exempt, that number will rise with the inclusion of the top 60 in the world rankings as of May 21 and June 11.
Non-exempt players will have a chance to earn their way to Shinnecock via qualifying, with established tour players advancing automatically to the final stage.
Woods and 11 other former champions are among those exempt from the rigours of qualifying.
The U.S. Open gives its champions a 10-year exemption, which means it stands alone among the four major championships.
U.S. Masters and PGA Championship winners earn lifetime exemptions, while British Open champions can play until they turn 60.
Woods, playing a full schedule again this year after a spinal fusion operation last April, will have plenty of opportunities to qualify for the 2019 U.S. Open at Pebble Beach via one of the other qualifying categories.
There are no guarantees, but the USGA routinely offers a couple of special exemptions to players it considers deserving.
Woods would no doubt fit that category, especially considering Pebble Beach was the scene of his most dominant performance. He won the 2000 U.S. Open there by 15 strokes.
That was one of his three U.S. Open victories, with his 2008 triumph at Torrey Pines in San Diego perhaps his finest moment, even if he played better in 2000.
Playing virtually on one leg with a badly damaged left knee and two stress fractures, he outscored everyone except Rocco Mediate over 72 holes, before winning a Monday playoff.
It was Woods' 14th major title, but he has not added to that number in the ensuing decade.
Woods tied for 17th at the 2004 U.S. Open at Shinnecock Hills.
(Reporting by Andrew Both in Cary, North Carolina; Editing by Ken Ferris)
