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La Trobe University professor of international relations Nick Bisley told CNN that Middle Eastern countries have begun to rethink their place in the world as the US begins to withdraw from the global stage.
"Israel and Saudi Arabia are the first part of a trend where, although the Middle East isn't going to change its name, it will be greater South West Asia, somewhere between the West and East," he said.
But Rodger Shanahan, research fellow at Sydney's Lowy Institute, said Israel and Saudi Arabia weren't about to abandon their close ties to the United States.
"One-off visits make a big splash and give the impression of significant engagement but ... if it's just a one off, it's not reorientation. It's just a toe in the water," he said.
'America First' pushes allies away
As a result, experts say, their allies may have decided to broaden their diplomatic options.
"People are hedging their bets a little bit because they think, with some foundation, the US is less inclined to dip into the Middle East militarily than in the past, so the feeling is they've got to be a bit more independent," Shanahan said.
Some countries are looking to cultivate new powerful friendships.
"From a Saudi point of view, if the US distances (itself) you'd want to find another great and powerful friend and China looks pretty good in that regard," Bisley said.
Middle East keen for Asian cash
For the oil rich Middle Eastern states, growing closer to Asia helps ensure their economic future.
"The Middle East has woken up to the fact that the world is changing quickly and Asia is now going to be the (economic) centerpiece of the world over the next 20 years," Bisley said.
But the economic benefits flow both ways -- Saudi Arabia and Israel are keen to be beneficiaries of Asian investment, especially China's One Belt, One Road program, which plans to link countries across Europe, the Middle East and Asia in an enormous trading network.
Experts say one of the best things for some Middle Eastern states is that Chinese investment and diplomatic closeness comes without Western nation's calls for human rights or democratic government.
"With China, there's no reason to talk about democracy," University of Sydney Adjunct Associate Professor Jean Jonathan Bogias told CNN.
"What they're going to do is provide assistance where assistance is needed and they'll look after China as they do so. And I think that will appeal."
Long way to go
There's still a long way to go though.
Despite their enthusiasm for Chinese investment, many Middle Eastern countries are wary of the Middle Kingdom's economic future.
"The feeling is that China will have to run out of steam at some point, so you don't want to overly dependent on Chinese investment, because that might not be long term," Shanahan said.
Some experts were also skeptical about a special relationship between Asia and the Middle East.
Shanahan said more high-level diplomacy would be needed first, including large economic deals to tie the regions together.
"You're going to have to look, over the next 12 to 15 months, what leaders visit other countries, what agreements are signed ... those are the kind of indicators that you'll need to look at to see if there's going to be any depth to what we've seen recently," he said.