Currently, he's using taxpayer's money.
According to this article by CNN, he will use federal funds initially.
Trump confirmed his plans to build the wall with federal funds and then seek reimbursement from Mexico, an idea Mexico has rejected. But negotiations, he said, would begin "relatively soon."
(emphasis mine)
Eventually, he still plans to let Mexico pay for it.
In an another article by CNN, he will use Mexicans' remittances to pay for the wall.
Trump has suggested some of the $25 billion in annual remittances that migrants return home would be retained to pay for the border wall -- a project Mexico opposes and which Peña Nieto has said Mexico would never pay for.
(emphasis mine)
This source of funding is possible since almost $25 billion was remitted from the US to Mexico in 2016.
Between January and November of 2016, $24.6 billion flowed back to the pockets of Mexicans from friends and relatives living overseas, according to Mexico's central bank.
However, some have expressed doubt.
Since the Mexican government won’t pay for the wall and holding up all remittances in order to get the Mexican government to pay for it runs into constitutional problems, some like Mark Krikorian of the Center for Immigration Studies have proposed a nation-wide refundable fee (a tax with another name) on wire remittances to fund the wall.
Taxing remittances of illegal immigrants will not raise enough funds for a huge new border wall.