"He will be in Moscow prior to Geneva 2," Riyad Haddad told the Interfax news agency, without specifying the date.
A diplomatic source in Damascus said the visit could take place on Thursday, AFP reported.
The announcement came as Russian Foreign Minister Sergei Lavrov held talks in Paris with US Secretary of State John Kerry about the Swiss conference, a follow-up to July 2012 consultations that failed to put an end to the fighting.
The Swiss meetings, due to begin January 22 in the Swiss lakeside town of Montreux and continue two days later in Geneva, are aimed at engaging Syrian government and opposition members in their first direct talks.
The July 2012 Geneva conference -- involving world powers but no Syrian government or rebel officials -- concluded with an agreement that Assad and his opponents should decide on a transitional government whose representatives suited all sides.
US officials interpreted the wording to mean that the deal excluded the possibility of Assad remaining in power.
But Russia -- its ties to Syria stretching back decades and involving weapons sales worth billions of dollars a year -- insists that Assad cannot be forced to step down through outside pressure because he retains strong domestic support.