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Barty could face former champion Garbine Muguruza in the third round and awaiting in the quarterfinals could be defending champion Angelique Kerber or seven-time winner Serena Williams with twice champion Petra Kvitova a potential obstacle in the semifinal.
Williams, a six-time US Open winner, romped to a 6-3, 6-4 victory over Croatian 22nd seed Petra Martic to set up a quarter-final with China's Wang Qiang, the conqueror of world number two Barty.
Serena Williams claimed her 100th win at the US Open in style, dismantling her quarterfinal opponent Wang Qiang 6-1, 6-0 in a blistering 44-minute performance.
Serena is chasing a 24th Grand Slam singles crown to equal the record held by Australian Margaret Court, but Mouratoglou said he had full respect for her final opponent Andreescu.
Andreescu beat Serena Williams 6-3, 7-5 in Saturday's final to maintain a 13-match unbeaten run, where she also won the Canadian Open, to break into the top 10 for the first time in her career.
The semi-final offered a classic matchup of styles with Williams and her prodigious power up against Svitolina, one of the best counter punches in the women's game.
Williams suffered her fourth consecutive defeat in a Grand Slam final at the US Open earlier this month.
The 19-year-old Andreescu became the youngest Grand Slam winner since Maria Sharapova at the 2006 US Open.
Serena Williams had the chance to equal Margaret Court's all-time record but instead it was Canadian teenager Bianca Andreescu who grabbed the trophy with a 6-3, 7-5 win.
Dropping only two sets in the entire tournament, the tenacious, power-hitting Andreescu barrelled through the competition at Flushing Meadows, showing no sign of a slowdown from a blockbuster summer.
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