Mr Trump has used almost every post-election speech to reiterate his promise to build a barrier separating his country from its southern neighbour.
Proposals are to be sought next month for the wall's design.
An executive order on 25 January for the wall's construction also asked government agencies to report on the financial assistance given to Mexico in the past five years.
This led to speculation Mr Trump may also divert US aid to pay for the wall.
But Mexico's foreign minister Luis Videgaray said his country would respond to any tax levied by the US and that they did not actually need financial help.
He warned Mexico could impose levies on select goods aimed at US regions most reliant on exports south of the border, such as Iowa, Texas and Wisconsin.
Speaking during a radio interview, Mr Videgaray said: "Without a doubt, we have that possibility and what we cannot do is remain with our arms crossed.
"The Mexican government would have to respond."
But he added that levies were "not our preference".
"Mexico believes in free trade."
Speaking about the prospect of losing US aid, Mexico's Interior Minister Miguel Angel Osorio Chong said his country now "has its own capabilities".
Most of US aid to Mexico comes through the Plan Merida programme, which has earmarked $2.6bn for security assistance of which $1.6bn has so far been spent.
Mr Chong said diverting the remainder of the aid would not come close to paying for the wall, which has an estimated price tag of $21.6bn.
He added: "We don't object to them moving these resources.
"When they realise what's left of Merida, they will understand that it's not even that significant."
Mexican anger towards Mr Trump has grown steadily since he first proposed the border wall, increasing with his insults about immigrants and calls on US businesses not to invest south of the border.
A plan to deport third-country nationals to Mexico sparked further outrage last week.
The plan would see non-Mexican nationals arrested along the border sent back to Mexico while their immigration cases were decided in the US.
Mr Chong told local radio: "They asked us if (non-Mexican illegal immigrants) could be here while they are going through the legal process there.
"We said that there was...absolutely no way."
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