The vote on the draft, which involved intense negotiations with Russia, Syria's main ally, is expected tomorrow.
Its presentation to the council was confirmed in a tweet by the Australian ambassador Gary Quinlan.
The text was sponsored by Australia, Luxembourg and Jordan and its supporters include Britain, the United States and France.
The text, a copy of which was obtained by AFP, calls on all parties to end sieges of densely populated areas immediately.
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The text also calls on all parties, in particular the Syrian authorities, to authorise UN agencies and NGOs access to swift, safe and unfettered humanitarian aide, including across frontlines and borders.
This cross-border access has been sought for some time by humanitarian groups so aid can be shipped directly into Syria from neighbouring countries such as Iraq or Turkey. The government has refused so far.
The resolution has no clause allowing for sanctions in case of non-compliance.
But it leaves this option open for the council if Secretary General Ban Ki-moon deems it appropriate. Ban would have 30 days once the text is passed to decide if additional measures are needed in case of non-compliance.