Both countries expelled their ambassadors in May 2018 over the killing of dozens of Palestinians by Israeli forces along the Gaza border and following Washington's decision to relocate its embassy to Jerusalem.
In December, Turkish President Recep Tayyip Erdogan said his country would like to have better ties with Israel but Israeli policy toward the Palestinians remained "unacceptable."
Erdogan champions the Palestinian cause, and has a contentious relationship with Israeli Prime Minister Binyamin Netanyahu.
Erdogan said then that Turkey had some issues with “people at the top level” in Israel, adding that Palestine still constitutes Turkey’s red line and that it was impossible for Ankara to accept Israel’s “merciless” policies regarding the Palestinian territories.
Turkey and Israel, once allies, have had a bitter falling out in recent years. Ankara repeatedly has condemned Israel's occupation of the West Bank and its treatment of Palestinians.
Dr. Hay Eytan Cohen Yanarocak, an expert on Turkey from the Jerusalem Institute for Strategy and Security (JISS) and the Moshe Dayan Center for Middle Eastern and African Studies (MDC) at Tel Aviv University, says it may be premature to say that things are going to happen soon.
Yanarocak says that despite the "constructive" signals that are coming from both sides, there won't be any major steps forward until the "crystallization" of the results of next month’s Israeli elections.
A change in leadership in Israel, he adds, may speed up the warming up of ties.
"If Israeli Prime Minister Binyamin Netanyahu will not be able to preserve his seat then, in Turkish eyes, launching a normalization with Israel will be far easier,” Yanarocak said.
Turkey also has criticized last years' normalization accords between Israel and four Muslim countries which were signed under US auspices.
Yanarocak says that these accords helped Israel to break out of its regional isolation, and has given it the upper hand in negotiating with Turkey toward improving diplomatic relations.
Hasan Awwad, an expert on Middle East politics at the University of Bridgeport in Connecticut, told The Media Line that there is much to gain from restoring diplomatic ties.
Last week, the first Israeli passenger plane, from the flag carrier El Al, touched down at Istanbul International Airport after a 10-year hiatus. This move can be seen as a signal that a thaw in relations is underway.
Awwad says the resumption of ties would have a major impact on the two countries’ defense industries.
"If the relationship is back to the same level as before the violent Marmara events, we would see closer cooperation in intelligence and commercially," he said referring to the Mavi Marmara incident, when Israeli forces in 2010 boarded a Gaza-bound flotilla carrying humanitarian aid for the Palestinians there that intentionally broke Israel’s blockade of the coastal strip, which ended in the death of nine Turkish activists on board.
That led to a decade-long freeze in relations between Turkey and Israel.
Yanarocak says having proper relations with Turkey is in Israel's "national interest."
But one major challenge to restoring relations between Israel and Turkey continues to be the Hamas movement.
Ankara is a supporter of the Islamist group that rules the Gaza Strip.
"In order to reach a ‘genuine normalization,’ the Israeli decision-makers are expecting Ankara to put an end to its support for Hamas," he said.
Mkhaimar Abusada, associate professor of political sciences at Al-Azhar University in Gaza City, told The Media Line that the Islamist "ideological links" between Hamas, which is part of the Muslim Brotherhood, and the Turkish government led by President Recep Tayyip Erdogan, who leads the Justice and Development Party in Turkey, are "difficult to break."
"I rule out that the improvement in the Israeli-Turkish relationship will come at the expense of Hamas. I think that it would have repercussions for Hamas, but nothing major," he said.
Abusada points out that Qatar, which he says supports the Muslim Brotherhood, has good relations with both Israel and Hamas.
"Qatar has always used its relationship with Israel to alleviate the human suffering in the Gaza Strip, which is ruled by Hamas. No one seems to object," he said.
But, he added, there may be some Israeli "demands to expel some Hamas leaders accused of supporting so-called terrorism, but in general, such relations in the end are in the interest of having the presence of mediators to be a link between Hamas and Israel."
But with shifting regional alliances such as the normalization deals between Israel and the UAE, Bahrain, Sudan and Morocco, and the reconciliation of Turkey's ally, Qatar, with the Gulf States including Egypt, may have persuaded Erdogan to re-think his foreign policy.
"Regional political changes are playing a major role. We are facing a stage in which regional differences melt away with the support of the White House and the new US administration, in addition to the great changes that the region is witnessing, such as the normalization deals, having an impact. Turkey does not want to be isolated in its surroundings," said Abusada.
Yanarocak says these new diplomatic ties may have played a role in forcing Turkey to re-think its policy on Israel.
"Thanks to the Abraham Accords Israel no longer feels isolated and, thanks to this new geopolitical fact on the ground, is feeling more confident to ask Turkey to make a comprehensive policy change vis-a-vis Jerusalem," he said.
The talk of closer ties with Israel comes at a time when Turkey's relations with both the US and Europe reached a low point.
Erdogan's conciliatory tone in recent weeks can be attributed to the changing of the guard in the White House.
"It is related to President Biden's victory,” Yanarocak said. “From the Turkish perspective, US-Turkish relations are in a very fragile situation as it has never experienced before and by mending the relations Turkey is planning to enjoy the Israeli influence on Capitol Hill to decrease the diplomatic pressure."
Erdogan had a cozy relationship with the former American president, with their relationship something of a “bromance” that had the two leaders constantly showering each other with praise. A Biden presidency is predicted to be more challenging for Ankara.
Former President Donald Trump bragged that world leaders came to him for help with Erdogan, saying Turkey’s leader listened only to him.
Turkey’s maritime claims in the Mediterranean are also a source of tension with Israel. Expecting the worst, Erdogan seems to be taking precautionary measures; for example, by signing a maritime border deal with Libya giving Turkey a path for exploration and pipeline construction in the Mediterranean.
Ironically, the two countries found common ground when they both backed Azerbaijan in its conflict with Armenia over Nagorno-Karabakh, the disputed, mainly ethnic-Armenian enclave in Azerbaijan. Israeli and Turkish drones and reported intelligence support from the two countries proved pivotal there in Azerbaijan's victory over Armenian forces backed by Iran.