The Syrian conflict is to be at the centre of intense diplomatic activity in New York, where world leaders are attending the UN general assembly.
Russian President Vladimir Putin is to hold rare talks with US President Barack Obama to outline his proposals.
Moscow has suggested there are plans to form an international contact group on Syria that will include Russia, the US, Iran, Turkey, Saudi Arabia and Egypt.
The Russians are a key ally of Syrian President Bashar al-Assad.
Western leaders have recently softened their stance towards him – conceding that he might be able to stay on during a political transition.
The threat of Islamic State (IS) extremists and the flow of Syrian refugees to Europe has added urgency to the search for a deal to end the civil war.
Russian deputy foreign minister Mikhail Bogdanov suggested both Russia and the United States would take part in peace talks on Syria next month, along with Egypt, Iran, Saudi Arabia and Turkey, the RIA Novosti news agency reported.
Mr Putin has reiterated his support for President Assad, who Western countries and the Syrian opposition have said must go.
A famous Russian expression talks about “killing two hares with one shot”. But Vladimir Putin doesn’t do things by halves: he’ll be trying to slay a whole multitude of political and economic hares with one trip to New York.
His UN speech and meeting with President Obama will put President Putin centre stage: a return to the international limelight for a leader shunned by the West over the conflict in Ukraine.
And if he convinces President Obama to put aside their differences and join together in the fight against Islamic State, Russia stands to gain on many levels: by retaining a degree of influence in Syria; by boosting Russian national security (Moscow acknowledges that IS constitutes a threat to Russia); and, crucially, by improving Russia’s international image – rebranding her from pariah to partner and refocusing attention from the conflict in Ukraine.
If Vladimir Putin achieves that, it could be the first step towards easing Western sanctions.
First, though, he will need to convince the US to trust him. It may be a hard sell.
Mr Putin, who has strongly reinforced Russia’s military presence in Syria, has called for a regional “co-ordinating structure” against IS, and said the Syrian president’s troops were “the only legitimate conventional army there”.
He said Russia would not participate in any troop operations in Syria.
Relations between Russia and the West have been strained over Moscow’s annexation of Ukraine’s Crimea peninsula last year and its support for separatist rebels in Ukraine’s east.
Mr Putin will also meet Iranian President Hassan Rouhani and Cuban President Raul Castro on the sidelines of the assembly, the Kremlin was quoted as saying by Reuters.
President Rouhani – a key regional ally of President Assad – says the government in Damascus “can’t be weakened” if IS militants are to be defeated.
US Secretary of State John Kerry, however, said the efforts were “not yet co-ordinated” and the US had “concerns about how we are going to go forward”.