U.S. President Donald Trump, speaks with Mohammed bin Salman, the Kingdom of Saudi Arabia's deputy crown prince and minister of defense, left, in the Oval Office of the White House in Washington, D.C., U.S., on Tuesday, March 14, 2017. Mark Wilson | Pool via Bloomberg

Reports of growing ties between Israel and Saudi Arabia have picked up in recent years. And now the two look set for further rapprochement, at least behind closed doors, as tensions in the Middle East escalate and interests among regional players create new geostrategic alliances. "Overt cooperation between Saudi Arabia and Israel seems unlikely, but an expansion of covert contacts and planning is highly likely," David Ottaway, Middle East fellow at the Wilson Center in Washington, D.C., told CNBC on Friday. Saudi Arabia's fairly muted reaction to U.S. President Donald Trump's declaration of Jerusalem as the capital of Israel on Wednesday — an official statement expressed "disappointment" in the decision — revealed both a continued desire to stay in Trump's good graces as well as a reluctance to stoke conflict with Israel, with which it officially does not have diplomatic relations. The Saudi government officially does not recognize Israel's existence as a state, and its powerful Wahhabi Muslim clergy is extremely hostile to the idea of a Jewish state. Yet a growing will to cooperate from both sides has become an open secret.

'The enemy of my enemy is my friend'

"What is driving them together today is the new priority Saudi Crown Prince Mohammed bin Salman is giving to showing Saudi resolve to stand up against Iran. This is being encouraged and facilitated by the Trump's strong anti-Iranian rhetoric and escalating U.S. military sales to the kingdom," Ottoway said. Indeed, the two countries have overlapping interests when it comes to stemming the influence of Iranian-supported proxies in Lebanon and Syria, namely Hezbollah and other Shia military and paramilitary forces.

In this handout photo provided by the Israel Government Press Office (GPO), US President Donald J Trump (L) and White House senior adviser Jared Kushner meet with Israel Prime Minister Benjamin Netanyahu (R) at the King David Hotel May 22, 2017 in Jerusalem, Israel. Getty Images

"It is probable that there is a U.S.-Israeli-Saudi plan in the making to agree on what steps each will take in parallel to roll back the influence of Iran and its proxies in Syria, Iraq, Yemen and Lebanon," Ottaway said. Israeli Energy Minister Yuval Steinitz in November confirmed contact between his government and Saudi Arabia's, but noted Riyadh's desire to keep it a secret. "We have ties that are indeed partly covert with many Muslim and Arab countries, and usually (we are) the party that is not ashamed," Steinitz said, as reported by Reuters. "When ties are developing, whether it's with Saudi Arabia or with other Arab countries... We keep it secret." In June, Israeli Intelligence Minister Yisrael Katz called on Saudi Arabia's King Salman to allow full diplomatic relations. Reports of rapprochement have also coincided with the growing influence of Deputy Crown Prince Mohammed Bin Salman, who is close to Washington, which is of course a key Israeli ally. NBC News reported in November that "U.S. diplomats engage with both sides with the assumption that the two parties speak directly," according to former senior U.S. officials. Daniel Shapiro, a former U.S. ambassador to Israel, told NBC there were "considerable amounts of quiet, behind-the-scenes coordination between them — intelligence channels and other security channels."

An awkward position

While the Saudi kingdom has not moved on any official engagement with Israel, "there is certainly strategic agreement that Iran and its militias in the region represent a threat to both countries and a natural drive to leverage this meeting of the minds," said Ayham Kamel, head of Eurasia Group's Middle East and North Africa practice. In a purely strategic sense, this would make Israel the kingdom's strongest potential Middle East partner in countering Iran for regional primacy. But any public cooperation would be extremely difficult and likely provoke a negative reaction, especially in light of Trump's Jerusalem announcement, said Ryan Turner, lead political risk analyst at Protection Group International.

Palestinian protesters burn the US and Israeli flags in Gaza City on December 7, 2017. Haniya called for a new Palestinian intifada, or uprising. This Zionist policy supported by the US cannot be confronted unless we ignite a new intifada," the head of the armed Palestinian Islamist movement that runs the Gaza Strip said in a speech. Majdi Fathi | NurPhoto

"Even in a country like Saudi Arabia where public dissent is limited, cooperation with Israel would carry major downside risks. Overt links would damage perceptions of the Saudi royal family at home and abroad, making it more likely that any rapprochement will be discreet and restrained," Turner told CNBC. "King Salman is probably disappointed with Trump's announcement (on Jerusalem) but the leadership in Saudi Arabia cannot afford to mobilize the Arab or Muslim population on the Jerusalem issue," Kamel added, stressing the Saudi monarchy's reliance on U.S. support for its regional endeavors.

'Completely under the radar'