By Simon Cambers

NEW YORK (Reuters) - World number one Roger Federer will begin his bid to win a record sixth consecutive U.S. Open title against American wildcard Devin Britton after the draw was made on Thursday.

The Swiss, who won the French Open and Wimbledon titles this year to set a record of 15 grand slam singles victories, is scheduled to play fourth seed Novak Djokovic of Serbia in the semi-finals.

"I am still playing very well," Federer said at the draw. "I played great in Cincinnati (where he won the Masters Series title last weekend) and I hope things can go well at the U.S. Open."

Second seed Andy Murray, runner-up last year and chasing his first grand slam crown, could face third seed Rafael Nadal in the semi-finals.

Women's champion Serena Williams begins her title defense against American wildcard Alexa Glatch.