The Democratic firm carried out the hypothetical match-up by "popular demand" after Rapinoe refused to visit the White House if the USA were to win the FIFA Women's World Cup.
What took place since the 34-year-old's comments saw Trump criticise the winger in a back-and-forth exchange, before extending an open invitation to the team, win or lose.
In the wake of Monday's (AEST) Women's World Cup final, won 2-0 by the USA against the Netherlands, Trump again took to Twitter to congratulate the team on their success, but it appears Rapinoe's stance on the matter remains unlikely to change.
"I don't think that I would want to go and I would encourage my teammates to think hard about lending that platform or having that co-opted by an administration that doesn't feel the same way and doesn't fight for the same things that we fight for," Rapinoe said.
While the Golden Ball winner and her teammates have since turned their attention towards equal pay, the PPP found she trumped the current president 42% to 41%.
The PPP also stated that voters who were undecided between the two figures had voted for Hillary Clinton in the 2016 election, suggesting further room for improvement in favour of Rapinoe.
"(Though) Rapinoe may be an unlikely presidential candidate, (her numbers) still speak to a broader truth about Trump’s standing – the fact that he polls in the low 40s against any Democrat ... shows that electability concerns are overrated," the PPP said.
