The reported promise, said to have been made in a phone call by Putin on Thursday, came on the day that Syrian President Bashar al-Asad begins a four-day official visit to Russia.
The Haaretz newspaper said Sharon had explained to the Russian leader that the weapons, also called Igla missiles, risked falling into the hands of Hizb Allah, which is opposed to Israeli occupation. Hizb Allah was successful in driving Israeli forces out of occupied southern Lebanon in May 2000.
Sharon's office had said on Thursday that the Putin-Sharon phone call centred on the situation in the Middle East, the unilateral Israeli plan of disengagement from the Gaza Strip, relations with Syria and Hizb Allah and their implications, and the recent election of Mahmud Abbas as Palestinian president.
The Syrian leader arrives in Moscow on Monday amid controversy over reports that Russia was ready to sell Syria, its long-time ally in the Middle East, state-of-the-art missiles capable of hitting any target within a radius that includes Israel.