Ahtisaari's proposal, which foresees "supervised independence" for Kosovo and is backed by Western powers, has prompted objections from permanent Security Council member Russia.
Russian Foreign Minister Sergei Lavrov has said Moscow would oppose the plan if Serbian interests are ignored.
In particular, Russian officials say Ahtisaari's plan does not go far enough in protecting the province's Serbian minority.
And some Russian observers have said the United Nations has not applied the same standards to Kosovo that it has to the frozen conflicts of Abkhazia, Transdneister, and South Ossetia.
But despite Russia's strong words, many analysts believe it is unlikely Moscow will use its veto on the Security Council.
RFE/RL Balkans analyst Patrick Moore says the major Western states will not allow Russia to block the proposal.
"I think that they [Russia] will bargain and cajole, but I also think that they realize that if they do cast a veto, the minute that they do so, they have lost their political capital in this particular affair," Moore says.
With the European Union and the United States backing the proposal, Russia has received criticism in the West for its stance on Kosovo. The EU has urged Russia not to stand in the way of the resolution and to exercise "responsible multilaterism."
Ahtisaari's plan offers conditional independence for Kosovo, with a constitution, a flag, and an anthem. The international community will still monitor the province, largely to protect the Serbian population.
Kosovo has been under UN control since 1999, after a NATO bombing campaign forced Serbia to withdraw troops accused of killing ethnic Albanians.
There are currently more than 15,000 NATO troops serving in Kosovo as peacekeepers.
The other unknown in the Security Council is China, although many analysts believe that Beijing is unlikely to be an obstacle.
The Security Council is expected to discuss Ahtisaari's proposal at a closed hearing in April.