Ukraine and Russia may hold technical-level talks at the Vatican next week.
Finland's president, Alexander Stubb, spoke to the country's public broadcaster, Yle, about the possibility on Wednesday.
His remarks came after he spoke by phone with Ukrainian President Volodymyr Zelenskyy and others following last week's high-level talks between Ukraine and Russia in Turkey.
Stubb reportedly said the United States has not stepped back from its role as a mediator, and that Europe is getting more involved in the ceasefire framework.
Senior officials from Ukraine and Russia held direct talks for the first time in three years last Friday. They made little progress toward a ceasefire deal, but agreed to a large-scale prisoner exchange.
Pope Leo XIV reportedly offered to host peace talks between the two countries at the Vatican. The new pontiff is calling for the peaceful resolution of conflicts in various regions.
Russian President Vladimir Putin sent a congratulatory message to the Pope after his election on May 8. Zelenskyy met him after his inaugural Mass on Sunday.