Malpass, who is now Trump's undersecretary for international affairs at the Treasury Department, has been a sharp critic of the 189-nation World Bank. He has argued that the bank, a lending institution with a focus on emerging countries, has concerned itself too much with its own expansion and not enough with its core missions, like fighting poverty.
Malpass would succeed Jim Yong Kim, who left in January three years before his term was to end.
Malpass, 62, made clear Wednesday that his focus at the World Bank would include furthering the Trump administration's agendas for developing countries.
"A key goal will be to ensure that women achieve full participation in developing economies," Malpass said. "I know Ivanka has been a strong leader on women's economic empowerment, and I look forward to continuing our work together on her women's global development and prosperity initiative.
In a meeting with reporters after Trump announced his nomination, Malpass sought to put his longtime criticism of the World Bank and its sister lending organization, the International Monetary Fund, into context.
He said his efforts going back to his service in the Reagan administration have been aimed at reforming both institutions. He pointed to the work he had done in the Trump administration to gain approval for a $13 billion capital increase for the bank, the first increase in eight years, a boost that included various lending reforms.
He said loans to those countries took away resources that should be going to poorer nations.
"I look forward to working with China and others on what the appropriate pace of that wind-down (of their loans) should be," Malpass told reporters.
The U.S. nomination of Malpass for the top job will go before the bank's board of directors on Thursday. He said he did not know whether other countries would put forward their own candidates but he said he would be traveling over the next several weeks to various countries to promote his candidacy, stopping first in China and Japan.
Since the World Bank and IMF were formed in the mid-1940s, the World Bank has always been led by an American and the IMF has always been led by a European. The United States is the largest shareholder in both organizations.
Senior administration officials, insisting on anonymity to discuss plans for the World Bank, said Malpass would evaluate bank programs based on such criteria as whether they helped raise median incomes and improved financial transparency.
Addressing climate change, which has been a priority for the World Bank, was pointedly not among the benchmarks of success that these officials named, though they said Malpass would honor existing initiatives.
Trump, who has been openly skeptical of climate change, announced in 2017 that he was pulling the United States out of the Paris Agreement, an international accord that created a framework for curbing carbon emissions.
AP Economics Writer Martin Crutsinger contributed to this report.