The number of applicants for the June 14-17 tournament is eclipsed only by the 2009 US Open at Bethpage Black (9,086), the 2010 US Open at Pebble Beach (9,052) and the 2005 US Open at Pinehurst (9,048).
"It is always gratifying to see how many golfers, from across the world, are interested in playing in the National Open Championship," USGA executive director Mike Davis said.
"The great appeal of the US Open is that anyone can enter, provided they meet the handicap index standards set forth."
To be eligible to enter the US Open, the second of the year's four Majors, a player must be a professional or have a handicap of 1.4 or better.
Northern Ireland's Rory McIlroy, the world number one, will defend the title he clinched in record-breaking style last year at Congressional where he triumphed by eight shots.
Eight other former champions are fully exempt for this year's edition: Angel Cabrera (2007), Michael Campbell (2005), Jim Furyk (2003), Lucas Glover (2009), Retief Goosen (2001, 2004), Graeme McDowell (2010), Geoff Ogilvy (2006) and Tiger Woods (2000, 2002, 2008).
Local qualifying for the US Open starts on April 30 at more than 100 venues after which 36 holes of sectional qualifying will take place at 13 venues from May 21 to June 4.
For the eighth year in a row, two of the sectional qualifiers are international. One will be held in Japan, on May 21, and the other in England, on May 28.