World Bank member countries reached a preliminary agreement on a 3.13 percent shift in voting power to give emerging and developing nations greater influence in the global institution.
World Bank officials, who agreed to talk on condition of anonymity, said the shift would increase the votes of the developing world to 47.19 percent.
There is a 99 percent chance this (deal) is closed, one World Bank source told Reuters.
The battle over influence at the aid-focused bank is part of efforts to reflect the growing clout of developing economies on the world stage and an important precursor to a similar move on the International Monetary Fund.
The agreement will be confirmed on Sunday when member countries convene at meetings on the World Bank's Development Committee. A final decision will be decided in a vote by member countries.
Nothing is done until our shareholder countries meet tomorrow at the Development Committee, World Bank spokesman Carl Hanlon said.
Earlier, IMF Managing Director Dominique Strauss-Kahn tipped journalists off to a possible World Bank agreement during a news conference, saying they achieved their shift in quota ... but at least I won't talk on behalf of Mr. Zoellick.
The 3.13 percent shift would amount to a contribution by the parties getting the extra power of about $1.6 billion in resources for the poverty-fighting global institution.
The talks have been difficult because advanced economies, especially those in Europe, have been unwilling to give up some of their voting shares, and the United States is holding on to its veto power.
Smaller European countries have been concerned that even a small change in their voting power would mean a marked reduction in their influence.
Earlier this week, World Bank President Robert Zoellick urged the Bank's 186 member countries to set aside differences to reach an agreement by Sunday, the last day of the IMF and World Bank meetings.
(Writing by Lesley Wroughton; editing by Patrick Graham)