Israel is on the Sunni side in the Sunni-Shia conflict. Not that Israel is pro-Muslim per se, but given the actual war going on between the proxies of Sunni and Shia Islam throughout the region, from Libya in the west to Yemen in the east, Israel is naturally on the side of the “moderate” pro-American Sunni States, notably Saudi Arabia, Jordan, Kuwait, Bahrain, the UAE and Egypt.
We might previously have included Syria and Iraq in this group, but how things have changed. Neither Syria nor Iraq exist as they did, both are engulfed in civil wars that pit pro-Shia and pro-Sunni elements against each other. Syria that is predominantly Sunni has been controlled by the pro-Shia Alawi Assad regime for 50 years, but its opposition is divided between the original insurgent Free Syrian Army of the democratic opposition, and the Sunni extremists of the Islamic State and Al Nusrah Front, that is an al Qaeda affiliate. It has been reported that there are actual contacts between Israel and the democratic opposition that has indicated it seeks good relations with Israel. The IS are strongly anti-Israel, but they are also strongly anti-Saudi and represent a true threat to the existence of these moderate Sunni States. In that case Israel and the Sunni States have a common enemy and a common interest in seeing IS defeated.
Under Saddam Hussein, Iraq was a Sunni-controlled state with a Shia Arab majority. Once Saddam was removed the Shia majority took over and their militias are currently fighting IS in central Iraq together with the Iraqi Army, having apparently taken Tikrit but recently lost Ramadi. But, the Iranian Revolutionary Guard (IRG) are fighting with the Shia in Iraq, in Yemen and with Hizbollah in Syria. So Iran also represents a real threat to the continued existence of the Sunni States in the region, and then we come to the potential nuclear threat of Iran.
Both the Sunni States and Israel recognize a power vacuum left by the loss of US deterrence in the Middle East under the Obama Administration. Further they recognize the danger of the current deal being touted by the Obama Administration between the P5+1 States and Iran. Even though Obama has stated numerous times that the US will not allow Iran to develop a nuclear weapon, the deal they have arrived at does not seem to very serious observers to satisfy this major aim. In this too the Saudis and their allies and Israel are on the same page.
So on all three counts, i.e. facing IS, facing Iranian aggression throughout the region and the Iranian nuclear threat, Israel and the Sunnis have common interests. I do not think that this can become an open alliance, but since Israel is by far the strongest military power in the region, and since when push comes to shove each country will look to its own interests, there could be and probably is informal contacts between these countries. For many years Israel has been the guarantor of Hashemite Jordanian survival against military threats from Assad’s Syria. In effect, this Israeli umbrella is being extended to the Sunni Arab States because of the lack of US deterrence and the imminent threats they face.