During the visit, Livni, who also serves as Israel's chief negotiator with the Palestinians, was to meet Russian Foreign Minister Sergei Lavrov in a bid to convince Moscow not to go through with the promised delivery, Israeli army radio said.
Livni's spokeswoman confirmed she was to meet with Lavrov in Moscow but denied it was in connection with the S-300 system.
The S-300 batteries are advanced ground-to-air weapons that can take out aircraft or guided missiles. The weapon could shoot down Israeli jets in the region or complicate any Western efforts to impose a no-fly zone over war-torn Syria.
The report came as Israeli commentators suggested an initial delivery of the surface-to-air system was likely to take place "in the next few weeks."
Israel is strongly opposed to Moscow supplying Damascus with such a system and warned it could take military action if it went ahead.
In early June, Israeli Defense Minister Moshe Yaalon claimed that Russia would not be able to deliver the anti-aircraft system to Damascus before 2014.
NTJ/BA