Ban "has been actively consulting" with all relative parties to the Syria issue, including the US, China, Russia, Britain, France as well as others, he told the RIA Novosti news agency during his visit to Moscow.
"We are still trying to look at a window possibility in early June but this is a matter of still further consultations," said the UN chief.
Foreign Minister Sergei Lavrov and US Secretary of State John Kerry agreed recently that Moscow and Washington would encourage Damascus and the opposition to discuss a political solution to the deadly two-year-old crisis.
Ahead of Ban's Russia tour, Moscow called for an urgent international conference on Syria and objected to setting up a no-fly zone in the country.
Earlier this week, Lavrov said that a possible meeting on Syria at a ministerial level may be held in Geneva if both sides of the conflict agreed to participate in the event
