To the question "Are you for or against handing over the Golan to Syria in exchange for peace?", 56% of respondents answered "no," while 36% supported the idea and 8% did not express an opinion.
The poll carried by the daily Maariv newspaper, and published on Friday, comes after a number of senior Israeli ministers argued that the talks frozen four years ago should be reopened.
Israel seized the strategic Golan plateau from Syria during the 1967 war and annexed it 14 years later.
Syrian President Bashar al-Asad has said he wanted to restart talks with Israel. Sharon has given the cold shoulder to the overtures. Some Israeli officials argue that the current regional situation is favourable to fresh negotiations.
The Maariv poll also revealed that the Israeli premier's popularity was on the rise since he announced his "disengagement" plan, which consists of unilateral measures Israel might take should the existing peace track with the Palestinians fail to bear fruit.
The percentage of people dissatisfied with Sharon's performance as prime minister dropped to 47 from 59 a month ago, the poll said.
The number of those satisfied rose to 41% from 33%. The survey was carried out on a sample of 605 Jewish and Arab Israelis and has a margin of error of 4%.