His comments on Wednesday were a response to a statement by the Syrian president the previous day which made it clear that he is willing to reopen stalled peace negotiations.
Bilateral peace talks collapsed nearly five years ago over the fate of the strategic Golan Heights plateau, which Israel occupied in the 1967 Six Day War and later illegally annexed.
However, Sharon told a press conference in Tel Aviv that he did not see "any real sign" that Syria wanted peace.
Elie Nisan, an Israeli television correspondent, told Aljazeera that Israel is willing to resume talks with Syria "if it stops harbouring Palestinian factions and terrorist organisations in Damascus, and stops directing terrorist organisations in Palestinian areas to carry out terrorist operations inside Israel".
Nisan said: "Syria keeps harbouring terrorist organisations, particularly Hizb Allah. Syria forms a bridge for transferring weapons from Iran to Hizb Allah."
He added: "When al-Asad gets serious, in talks and actions, to have peace with Israel, the Golan issue and related relinquishments will then be suggested."
"negotiations [with Israel] should resume at the point where they broke off in January 2000".
During a telephone conversation with Lebanese President Emile Lahud on Tuesday Bashar al-Asad said
The Golan Heights were illegally
annexed by Israel in 1981
Also on Tuesday, Syrian state newspaper Tishrin expressed "Syria's real desire to bring about a just and lasting Middle East peace and needed only Israel's desire" to do the same.
And SANA, the official news agancy, quoted an official confirming that Damascus wanted to continue talks where they left off five years ago, "taking into account what has been achieved ... including the Rabin offer".
Syria has said Israeli prime minister Yitzhak Rabin, who was assassinated in 1995, offered a complete return of the Golan in exchange for normalisation in relations with Damascus.
The government in Damascus has poured cold water on Israeli claims that Palestinian factions in Syria direct operations inside the Palestinian territories, saying that the Palestinian resistance is home-grown.
Al-Asad: Talks must start from
where they broke off in 2000
It has also defended Hizb Allah as a legitimate counterbalance to what it calls Israel's hegemonic ambitions.
Syria's apparent readiness to resume peace talks comes as Israel is gearing up for a full evacuation of the Gaza Strip next year.
Observers doubt if Sharon will ever let Israel get bogged down in peace talks with Syria or contemplate any withdrawal from the Golan while preoccupied with the Gaza pullout.