The 21-year-old Pole on Thursday saw off China's Qinwen Zheng 6-4, 4-6, 6-1 in their second-round match in San Diego, notching up her 61st win of the year.
Meanwhile, Gauff, who is ranked world No. 8 by the Women's Tennis Association (WTA), defeated Canadian Bianca Andreescu 6-4, 4-6, 6-3 in the second round of the women's tournament in California to set up a clash with the Polish star.
Świątek, who is the top seed in the tournament, had a bye in the first round.
The Polish player last Sunday lost the final of the Ostrava Open tennis tournament in the Czech Republic to home favourite Barbora Krejčíková.
The Polish world No. 1 was upset by the 26-year-old Czech 7-5, 6-7, 3-6 in the championship match, failing to claim her 11th career singles title and ending her 10-match winning streak.
Świątek last month won the US Open, capturing her third Grand Slam trophy.
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Source: IAR, PAP