The current president of the financial institution, Jim Yong Kim, announced that he would be cutting short his tenure on Monday, more than three years before his second term was due to end.
Ivanka Trump was in 2017 behind the World Bank's $ 1 billion fund to promote women's business initiatives.
Ivanka Trump, 37, serves as a senior adviser to the president; she shut down her own fashion label in July, saying that she would focus on her job in the White House.
The Times reported that other candidates for the position include former United Nations Ambassador Nikki Haley and current Treasury official David Malpass.
The Treasury Department told AFP on Friday that it had no comment on potential candidates.
According to a long-standing tradition, the World Bank is led by an American pick: the United States nominates the president as the largest shareholder in the financial institution.
"We are beginning the internal review process for an American nominee, and we look forward to working with the governors to elect a new leader", he said.
But the success of a USA candidate no longer appears completely assured.
The World Bank is about to be leaderless.
The bank's board said its selection process will be 'open, merit-based and transparent, ' suggesting that non-US contenders would also be considered.
However, some pundits say that the worldwide financial community is not prepared for a non-American nominee at the moment.
The World Bank Board said Thursday it would start accepting nominations for a new leader early next month and name a replacement for Kim by mid-April.