It urges countries to "move vigorously and decisively to cut the flow of funds" to IS, such as by preventing its smuggling of oil and antiquities.
The militant group is widely believed to be the world`s wealthiest.
A recent study estimated that it its monthly revenue was $80m (£53m).
`Comprehensive strategy`
Thursday`s summit of finance ministers of the UN Security Council in New York will be the first in the international body`s 70-year history.
The US and Russian-drafted resolution they are expected to be approve unanimously will rename the committee monitoring sanctions against al-Qaeda as "the Isil (Daesh) and al-Qaeda sanctions committee", using acronyms based on the group`s previous name in English and Arabic.
Any individual, group, undertaking or entity supporting the groups and their offshoots will be subject to UN sanctions, including an asset freeze, travel ban and arms embargo.
The draft encourages all countries to "more actively submit" names for inclusion on the sanctions list and to share information about extremist groups.
It also requires them to report within 120 days on what steps they have taken to curb the financing of IS, and asks UN Secretary-General Ban Ki-moon to provide a "strategic-level report" in 45 days on the sources of revenue for IS.
A similar resolution was passed by the Security Council in February, but diplomats complain that it has been routinely flouted.
Writing in the Daily Telegraph on Wednesday, UK Chancellor George Osborne and Foreign Secretary Philip Hammond said isolating IS from the international financial system "must be a key element of any comprehensive strategy to degrade and ultimately destroy it".
"Seizing territory in eastern Syria and western and northern Iraq has allowed Daesh to take control of a large number of oilfields. It extracts oil not only for its own use, but also for sale at discounted rates to middlemen," they added.
"Indeed, the Syrian oilfields are thought to be providing Daesh with around $1.5 million a day. We know that the military action we are now taking with our allies, targeting oil infrastructure, is starting to limit this resource. But we can and should do more."
Last week, analysis by IHS suggested that the overall monthly revenue generated by IS was $80m, with around 50% coming from taxation on the profits of all the commercial activities in areas under its control and the confiscation of land and properties; and around 43% from the smuggling of oil and gas.
Other sources of revenue were the trafficking of drugs and antiquities; carrying out criminal activities, including bank robbery and kidnap for ransom; running small enterprises; and donations.
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