In the letter, written after a G20 summit in Turkey and seen by Reuters, Juncker underlined the importance he attached to good relations between the European Union and Moscow, "which to my regret have not been able to develop over the past year," Reuters reports.
He said he had asked Commission officials to study options to bring the EU and the Eurasian Economic Union - a grouping of former Soviet states dominated by Moscow - closer together.
"The decision on the circumstances in which to proceed along this path is in the hands of the member states of the European Union and should in particular be synchronized with the implementing of the Minsk agreements," Juncker wrote.
Read alsoObama, Putin hold unscheduled talks at G20 summit; discuss Ukraine, Syria: APThe initiative could offer Putin an incentive to cooperate in Ukraine at a time when France and some other west European states are trying to re-engage with Moscow after the Paris attacks to fight Islamic State and forge a peace deal in Syria.
Lithuanian Foreign Minister Linas Linkevicius said he was surprised by the letter, which he said did not reflect a common view of EU member states and made no reference to EU sanctions against Russia over its annexation of Crimea and the destabilization of eastern Ukraine.
Read alsoSteinmeier: Russia focusing efforts in Syria, taking attention away from UkraineBaltic and central European member states are worried that the EU executive and west European partners may be preparing to let Moscow off the hook of sanctions over Ukraine in return for cooperation in the Middle East.