There will be no Andy Murray, who retired from the sport after his Olympic men’s doubles quarter-final defeat in August.
British number two Cameron Norrie is also missing with a forearm injury.
Jack Draper, the British number one, will be seeded for the US Open, with Dan Evans also in the main draw.
Katie Boulter is the top-ranked Briton in the women’s draw, with Emma Raducanu and Harriet Dart also making the cut.
In the men’s doubles, Joe Salisbury and American partner Rajeev Ram are the three-time defending champions.
Eight other Britons are attempting to reach the main draw through qualifying, as mentioned above.
American captain Bob Bryan has been ribbed by tennis fans for a selection gamble that backfired massively as Australia reached the Davis Cup semi-finals for the
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