“Paying for a wall is not part of our vision,” foreign minister Claudia Ruiz Massieu told local television on Wednesday.
As part of his campaign, Mr Trump vowed that he would build a massive border wall and make Mexico pay for it.
Ms Ruiz Massieu said that the government had maintained communication with Mr Trump’s campaign team ever since his visit to Mexico in August.
“There has been a fluid, daily communication with different members of the campaign,” she said.
Mexico’s President Pena Nieto said he was ready to work with Mr Trump to help bilateral relations, and that the two countries would continue to tighten bonds of cooperation and mutual respect.
Mr Nieto was heavily criticised for receiving Mr Trump in Mexico during the campaign, after the Republican candidate called Mexican immigrants rapists.
“Mexico and the United States are friends, partners and allies and we should keep collaborating for the competitiveness and development of North America,” Mr Nieto said on his Twitter account.
Mr Trump has said he could tear up the North American Free Trade Agreement (NAFTA), which has increased commerce between Mexico, the United States and Canada, saying that it has killed US jobs.