Secretary of State Cardinal Pietro Parolin was quoted by Reuters as making the comments during a joint press conference in Moscow with Russia's Foreign Minister Sergei Lavrov.
The pope has been keen to strengthen ties between Catholic and Eastern Orthodox churches - which split apart near one thousand years ago.
Cardinal Parolin said further work must be done in order for the trip to become a reality and he didn't name any potential date for a visit.
In the first summit of its kind Pope Francis and the Patriarch of Russian Orthodox Church Patriarch Kirill met in Cuba last year. The fact the trip went ahead was hailed as a signal of improving relations between the Vatican and the Kremlin.
During his four-day visit to Russia, Cardinal Parolin has met with Patriarch Kirill. He is also due to meet President Vladimir Putin in the Black Sea resort in Sochi.
In Tuesday's meeting Cardinal Parolin and Mr Lavrov agreed on a need for further dialogue to help resolve a political crisis currently gripping Venezuela. They also announced a visa-free travel agreement for Vatican and Russian diplomatic figures.