The bombastic billionaire has promised to crack down on illegal immigration and insulted Mexican immigrants by calling them rapists, criminals and drug dealers.
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As his party's presumptive presidential candidate, Trump is now eyeing a clash in the November election with his Democratic rival Hillary Clinton.
"There is no way to have Mexico pay (for) the wall. But any decisions inside (the) USA -- is a decision of its government," Pena Nieto told CNN in English.
The Mexican president earlier had said Trump's campaign pledge was a non-starter, but he did not address the issue as specifically.
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Pena Nieto said US-Mexican relations were based on coordination, collaboration and cooperation on security issues.
The Mexican president earlier compared Trump's rhetoric to the rise of European dictators Adolf Hitler and Benito Mussolini.
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