US Senator Arlen Specter (R-PA), who held a high-profile meeting with Syrian President Bashar Assad on Sunday, was interested in bringing a message to Assad from Prime Minister Ehud Olmert, but was told that the necessary messages had already been sent, The Jerusalem Post has learned. Specter said after the meeting that he had the sense that Assad and Syrian public opinion were ready for peace, and that the US could help "bridge the gap" between Israel and Syria. Specter met Olmert last week before going to Syria. The US senator said in Damascus that "the core of the deal" would be a return of the Golan Heights. On Tuesday, the London-based Arabic newspaper Al-Hayat quoted Syrian sources as saying that "Damascus has decided to pursue real peace with Israel which will give Syria its rights back." According to the paper, the sources said that in order to move the process forward, "Israel must guarantee the return of the Golan Heights to Syria." The paper implied that negotiations between Damascus and Jerusalem were currently under way via Turkish mediation, and that if the negotiations were successful, the US would be asked to participate in direct Israeli-Syrian talks. Israeli officials said Syria was interested in high-profile talks in order to get the US involved and improve its relationship with Washington, while Israel was interested in pursuing more discreet back-channel talks - away from the public eye - to test Syria's sincerity. Olmert, in an interview with the Post that will be published on Friday, said peace with Syria was in Israel's interest because it would pull Syria away from Iran, Hizbullah and Hamas. However, he added that the Syrians had to decide whether they were prepared, and that he was willing to "check whether it is possible to conduct a serious, deep and true discussion" with Damascus. "They say they want to make peace. I hope they mean what they say," Olmert said. Olmert did not set preconditions to holding talks with Syria, but added, "There will not be peace with Syria if Syria is connected to Hamas, Hizbullah and Iran and continues to encourage the actions it is encouraging. That is perfectly clear. It's either-or."