Rapinoe has stood next to her team-mates during the national anthem, though she has still faced criticism for not singing it or putting her hand over her heart.
When asked if Rapinoe's actions were appropriate, Trump told The Hill's Jordan Fabian and Saagar Enjeti: "No. I don't think so."
Rapinoe began protesting in solidarity with former NFL quarterback Colin Kaepernick, who started kneeling during the anthem in 2016 to protest against racial injustice and oppression in the United States.
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Per ESPN.com, the United States Soccer Federation made it a requirement that players stand during the anthem after Rapinoe began kneeling.
The women's team also filed a lawsuit against the Federation in March citing gender-based discrimination in pay.
Trump said the issue should take into consideration "the economics," as the biggest stars in the men's game like Cristiano Ronaldo "draw hundreds of thousands of people."
However, he added: "But I haven't taken a position on that at all. I'd have to look at it."
Rapinoe dispatched two penalties as the USA saw off Spain 2-1 in the round of 16 on Monday, and she reflected on the match:
The 33-year-old, who has described herself as a "walking protest" against Trump, is eagerly anticipating Friday's quarter-final with hosts France at the Parc des Princes in Paris.
Per Goal's Seth Vertelney, she said:
"Hopefully [it's] a complete spectacle, just an absolute media circus. I hope it's huge and crazy, that's what it should be.
"I hope it's just a total s--tshow circus. It's going to be totally awesome.
"I think this is what everybody wants, these are the biggest games that you dream about as a kid."
Alongside the U.S., who are the defending champions after winning the World Cup for the third time in 2015, France are among the favourites for the tournament.
Les Bleues won all three matches in the group stage as they saw off South Korea, Norway and Nigeria. In the round of 16, they beat Brazil 2-1 after extra time on Sunday.
Their clash with the Americans on Friday could be one of the best matches of the tournament. It might also have a significant say in who goes on to lift the trophy, and Rapinoe will be key to the USA's efforts.