The suggested changes are related to Moscow's refusal to support the ouster of Syrian President Bashar al-Assad, diplomats said on condition of anonymity.
Russia and the other permanent U.N. Security Council members told Annan this week they support a transitional Cabinet that could include government and opposition members but would "exclude ... those whose continued presence and participation would undermine the credibility of the transition and jeopardize stability and reconciliation," according to Annan's proposal.
Diplomats told Reuters that Annan's idea of excluding certain people was clearly referring to Assad, though the proposal does not explicitly say the Syrian president could not serve in a national unity government.
Annan's proposal for a political transition aimed at ending the 16-month conflict in Syria is one of the main issues that Russia, the other four permanent Security Council members and key players in the Middle East planned to discuss at a high-level meeting in Geneva on Saturday.
Although Russia signaled to Annan this week that his plan was acceptable to Moscow, Russian Foreign Minister Sergei Lavrov reversed course on Thursday, diplomats said. He publicly complained on the Foreign Ministry's Twitter feed about the way details of Annan's proposal were leaked to the media.
"Any leaks to press from draft report on Annan plan are evidence of unscrupulous diplomatic practices," Lavrov said.
Diplomats said the Russians have now demanded that Annan remove from his proposal the language about excluding people from a Syrian national unity government, an amendment they said was unacceptable.
Annan and the Western delegations were encouraging Moscow to drop the demand, envoys said, adding that the issue would certainly come up when Lavrov and U.S. Secretary of State Hillary Clinton meet in Russia on Friday.
One diplomat said the Russians were now "walking back" from their earlier for support for Annan's proposal. They said the United States, Britain and France had waited until Russia informed Annan of its acceptance of his political transition proposal before agreeing to go to Geneva to discuss it.
A senior Western diplomat said the United States, Britain and France were getting "mixed messages from Russia, which could put the Geneva meeting in doubt."
The language about excluding certain people is the whole point of Annan's political transition plan, which cannot be credible if it leaves Assad in power, the envoys said.
"Without that sentence about exclusions, there's no transition plan," said one diplomat.
Moscow has refused to abandon Assad, a staunch Russian ally and major purchaser of Russian weapons.
Another amendment suggested by Russia, which Western diplomats said was equally unacceptable, was to include a call on the Syrian government and the opposition to stop fighting simultaneously.
"Obviously the government has to stop fighting first," a Western diplomat said.
Russia's U.N. mission was not immediately available for a response.
Annan had made preliminary acceptance of his guidelines for a political transition for Syria a condition for organizing Saturday's meeting in Geneva. The meeting is to include the United States, Britain, France, Russia, China, Turkey, Iraq, Kuwait and Qatar. Iran and Saudi Arabia were not invited.
Senior diplomats from the countries attending the meeting will gather in Geneva on Friday to try to prevent any collapse of Saturday's ministerial-level talks.
Russia has repeatedly said it supports Annan's idea of creating a "contact group" of powerful nations and regional players with influence on the Syrian government or the opposition to push for an end to the violence in Syria.
Moscow has also said it is not insisting that Assad must remain in power at all costs, but that any decision on whether or not he should step down should come from the Syrian people, not from outside pressure or military intervention, as happened last year in Libya.
The United States, Britain and France have said that Assad is responsible for the violence, which the United Nations estimates has killed at least 10,000 people, is no longer fit to govern. Russia and China, however, reject what they describe as Western calls for "regime change."