"Neutral status is now being seriously discussed along, of course, with security guarantees," Foreign Minister Sergei Lavrov said told RBC news.
"Now this very thing is being discussed in negotiations - there are absolutely specific formulations which in my view are close to agreement," Lavrov said.
He said that President Vladimir Putin had spoken about neutrality, along with security guarantees for Ukraine without NATO enlargement, as one possible variant in February.
The euro extended gains after Lavrov's comments and was up 0.4 percent to $ 1.1005.
Lavrov cautioned that the negotiations were not easy but that there was "some hope of reaching a compromise".
Ukraine has also made cautious positive statements on peace talks. It says it is willing to negotiate to the end the war, but will not surrender or accept Russian ultimatums.
On Feb. 24, Putin blamed the United States for threatening Russia by enlarging the NATO military alliance eastwards into Russia's backyard.
Putin said there was no option but to launch the military operation because Russian-speaking people in Ukraine had been subjected to genocide by "nationalists and neo-Nazis" since Russia's 2014 annexation of Crimea.