The vote on the resolution in the General Assembly could happen as early as April 26 although no official date for the vote has been confirmed, the source said.
The resolution is being put forward by Liechtenstein and has received co-sponsorship from over 50 countries including the United States. If passed, the five permanent Security Council members would be required to justify their use of veto powers.
The resolution comes amid criticism of Russia by US ambassador to the UN Linda Thomas-Greenfield and others for purported abuses of its veto power on the council.
Western countries in the UN Security Council and General Assembly have repeatedly expressed dissatisfaction with the way China and Russia used their veto power, preventing the adoption of Western-backed resolutions.
One of the latest examples was the resolution of Western countries condemning the Russian special military operation in Ukraine. Moscow vetoed it.
Unlike UNSC decisions, UNGA resolutions cannot prescribe coercive measures against nation-states.