Sharon is due to arrive in Moscow on Sunday.
His three-day visit comes as Russia prepares to submit a resolution to the UN Security Council making the implementation of the internationally-backed blueprint compulsory.
Together with the United States, United Nations and the European Union, Russia is one of the so-called quartet of diplomatic players to back the "road map" for peace in the Middle East.
Russia's UN ambassador Sergey Lavrov said he wanted to get the resolution adopted by "consensus" on the often divided council by next week, "exactly at the time the government is going to be formed" by Palestinian Prime Minister Ahmad Quraya.
But the US has given initial indications that it would not back the proposed measure.
"It is unnecessary to involve the UN in such a way, because it can only deal a fatal blow to the 'road map'," one high-ranking Israeli official told AFP on condition of anonymity.
He said that the United Nations, "which takes a consistently anti-Israeli stance, would demand the implementation of the commitments included in the 'road map' only from Israel, whilst ignoring the Palestinians' actions".
The "road map" was published on 30 April and formally accepted by both parties but Israel has drawn up a list of 14 reservations to the document.
The blueprint calls for an end to all "violence", a total halt of Israel's settlement activity and an army withdrawal to pre-Intifada lines, as part of measures paving the way to the creation of a Palestinian state by 2005.
Russia and Iran
The other major issue Sharon will broach during his visit is Iran's nuclear activities, which Israel sees as the greatest strategic threat to its security.
"We are going to try to convince the Russians of stepping up their control over the technology transfer to Iran and the presence of Russian nuclear experts in Iran," the Israeli official said.
"We are going to convince the Russians of steping up their control over the technology transfer to Iran..."
During his last visit to Moscow in September 2002, Sharon obtained guarantees from Putin that Russia was taking all necessary steps to prevent the transfer of nuclear technology to Iran.
Russia is building the Bushehr reactor in southern Iran in bilateral cooperation that Washington fears will hand nuclear capability to the Islamic republic.
The head of Israeli military intelligence, General Aharon Zeevi, said on 21 October that the "Iranian nuclear programme will reach its point of no return within 10 months. After that period, international diplomatic measures will not be able to stop the programme".
Analysts said at the time that Zeevi, who had been speaking to parliament's defence and foreign affairs committee, had also suggested that Israel might "take upon itself to stop the Iranian military nuclear programme if international pressures failed."
In 1981, Israeli warplanes put an end to then Iraqi president Saddam Hussein's nuclear programme, bombing the Osirak facility near Baghdad.
Israel might "take upon itself to stop the Iranian military nuclear program if international pressures failed"
General Aharon Zeevi,
chief of Israeli military intelligence
Sharon is also expected to hold meetings with Russian Prime Minister Mikhail Kasyanov, Foreign Minister Igor Ivanonv and Defence Minister Sergei Ivanov.
Accompanying Sharon on his trip will be Absorption Minister Tzipi Livni and Transport Minister Avigdor Lieberman, who chairs the Israeli-Russian economic council.