Davutoglu said Israel's 2008 invasion of Gaza scuttled a potential peace deal after Turkey mediated in indirect talks between Israel and Syria.
"Is it possible to restart it again? Yes, why not?" Davutoglu said in response to a question about the talks.
"If the two countries agree to restart it, we can do it. As Turkey, we are ready," Davutoglu said at the International Institute of Strategic Studies think tank in London.
"The Syrian side already declared they want to continue from where we left (off). The Israeli side, they have different views. Some coalition members are against, some are in favor. We will see," he said.
"If we see a strong political will, both in Israel and Syria, we will continue to support (peace efforts). We will support every attempt, step in the direction of peace."
Israel and Syria held four indirect rounds of peace talks with Turkish mediation in 2008, but they were suspended following the resignation of then Israeli Prime Minister Ehud Olmert in September that year.
Syria said at the time of the Israeli offensive in Gaza at the end of 2008 that it ruled out a resumption of the indirect talks any time soon.
But more recently, Syrian President Bashar Assad has expressed interest in renewing negotiations with Israel.
Syria wants an Israeli commitment to withdraw from the whole of the Golan Heights, the Syrian plateau that Israel occupied in the Six-Day War.
Israel has said it was willing to resume the talks without preconditions.
George Mitchell, US President Barack Obama's Middle East envoy, discussed reviving peace talks between Israel and Syria last week with Assad, who said Israel had to "declare frankly" it wants peace.
Muslim but secular, Turkey has a history of military cooperation with Israel and has acted as an intermediary for the Jewish state with the Arab world.
But relations have soured recently as Turkey repeatedly criticized Israel's offensive in Palestinian-ruled Gaza.
Syria has meanwhile improved its ties with Turkey, making Israeli officials wary of Turkey resuming a mediation role.
Davutoglu repeated that the Israel-Syria peace talks had been making progress when Israel launched the Gaza offensive.
Turkey was "concerned with the policies of Israel because of Gaza," he said, adding: "Criticizing one policy of an Israeli government does not mean the end of Turkish-Israel relations."