The Americans are keen for strategic reasons to have the two non-Arab military powers in the eastern Mediterranean back together to possibly restore a modicum of stability in a region that's swirling with conflict, sectarian hatreds and political turmoil.
Obama is to visit Israel in March. Kerry is on his maiden trip as top U.S. diplomat and is to visit Ankara, where he's expected to raise the issue of Turkish-Israeli relations.
There appears to be an effort by both sides to patch up a relationship, encouraged by the United States which viewed the Turkey-Israeli alliance as vitally important for regional stability.
But Israel and Turkey are also being nudged toward reconciliation by the growing turmoil in the region, particularly Iran's confrontation with the United States and Israel, and the increasingly dangerous civil war in Syria.
Israel and Muslim Turkey forged a discreet alliance that began in 1984 but became a full-blown strategic partnership in 1996.
But the entente began to fray after Turkey's 2002 parliamentary elections when the Islamist Justice and Development Party gained power under Recep Tayyip Erdogan.
The new prime minister was uncomfortable with the close links that Ankara had established with the Jewish state through Turkey's powerful military establishment, with U.S. blessings.
Erdogan was impatient with Israel's foot-dragging in the peace process and the continued occupation of Palestinian land.
The break came in May 2010 when a Turkish-organized flotilla of ships carrying humanitarian aid for the blockaded Gaza Strip was intercepted by the Israeli navy in international waters of the Mediterranean. Naval commandos killed nine Turks aboard a Turkey ship, the Mavi Marmara.
Israel refused Ankara's demands for a formal apology and compensation, claiming it acted in self-defense.
Erdogan withdrew his ambassador, scrapped major military contracts worth billions of dollars to Israel's export-hungry defense industry, and halted all military training cooperation with Israel.
The Jerusalem Post reported that Israeli Prime Minister Binyamin Netanyahu's government has sent messages to Ankara over the last two weeks on the need to "get more positive vectors" in their relations.
There were no other details, and given the popular animosities stoked up in both nations since 2010, there's not likely to be because Netanyahu, who's trying to stitch together a governing coalition as Israel's isolation grows, and Erdogan, with overwhelmingly pro-Palestinian electorate, must both tread carefully.
Erdogan's been striving to restore Turkey as a paramount regional Muslim power and making up with Israel is unlikely to impress his neighbors.
But wider strategic issues are at stake with the bloodbath in Syria threatening to engulf neighboring Turkey, Jordan and Lebanon amid Arab turmoil.
Despite the vitriolic barbs Israel and Turkey have hurled at one another since 2010, there are senior officials on both sides who've been quietly seeking to end the rift.
Israel's outgoing defense minister, Ehud Barak, the country's most decorated war hero, has consistently worked for a rapprochement, no doubt with substantial defense sales and access to important training programs in mind.
On Feb. 17, the Turkish newspaper Today's Zaman, reported Israel, under U.S. pressure, had allowed the delivery of electronic warfare suites for two Turkish AWACs that had been blocked in 2010.
Two days later, Turkey's Radikal newspaper reported secret talks under way to find an accommodation, with Israel prepared to issue an apology for the Mavi Marmara killings, possibly timed with Obama's visit.
There have been other reports of secret talks in Geneva and Cairo.
"Turkish-Israeli reconciliation has, at least for a while, been an important item on the U.S. foreign policy agenda in the Middle East," observed Mideast analyst Ramzy Baroud.
"Neither Turkey and Israel, nor the U.S. and NATO are able to sustain the status quo -- the rift between Israel and Turkey -- for much longer.
"But returning to an old paradigm, where Turkey is no longer an advocate of Palestinian rights and champion of Arab and Muslim causes, could prove even more costly," Baroud noted.