He added that any coalition partner would have to agree to the National Health Insurance (NHI) Bill, which was signed into law earlier this month.
The DA opposes both the NHI and the ANC's black empowerment policies.
The DA's support appears to have grown in this election, with the party having regained the votes of white people who had backed a party to its right in the last election, and some black people who felt it needed to be given a chance in national government.
Despite the ANC's reluctance to align with the DA, its leader John Steenhuisen hasn't ruled out the idea.
Mr Steenhuisen said if an alliance with the ANC was reached there would be a few non-negotiables.
"Respect for the rule of law and the constitution, a social market economy that treats the private sector as partners in the growth agenda.
"Zero tolerance for corruption and cadre deployment, and an absolute laser-like focus on economic policies that grow jobs."
Mr Steenhuisen also told the BBC he would have to consult pre-election coalition partners before considering any negotiations.
But he ruled out the EFF and the MK party, which both advocate seizing white-owned land and nationalising mines, as potential coalition partners.
"I think instability is not in the best interest of the country. A coalition with the radical left in South Africa of the MK party and the EFF will produce the same policies that destroyed Zimbabwe, destroyed Venezuela," he said.
One possibility would be a coalition between former MK party and the ANC in both KwaZulu-Natal and nationally - but given the fractious relations between the two parties, that appears unlikely.
While Mr Zuma has been suspended from the ANC, he is still a member. He appeared to suggest he would to do a deal with the ANC if it replaced President Cyril Ramaphosa as leader.
"I've got the problem with the leadership of the ANC, not with the ANC itself or its membership," he told the BBC recently.
He was however reluctant to discuss the prospect of entering into a post-election pact with the ANC.
Another option would be to work with the EFF, led by Julius Malema, a former ANC youth leader. The two parties currently form the coalition that runs the country's biggest city, Johannesburg.
A record 70 parties and 11 independents were running, with South Africans voting for a new parliament and nine provincial legislatures.
The DA has signed a pact with 10 of them, agreeing to form a coalition government if they get enough votes to dislodge the ANC from power.
But this does not include the EFF or MK, who would be needed to form a majority.
As the parties scramble to form alliances, Kenya's former President Uhuru Kenyatta, who is leading the African Union election observer mission in South Africa, offered some advice for forming coalitions.
He said coalition governments need to focus on areas of agreement instead of differences.
"I can only wish them well and hope that the leadership will take this decision by the people in a positive frame," he said.