Swedish prosecutors have issued an international arrest warrant for Assange over allegations of rape, charges he has denied and has hinted could be part of a "smear campaign".
The 39-year-old Australian is believed to be in Britain, and a report said he could be arrested this week.
Assange broke cover on Friday to say in an online chat that he had boosted security after receiving death threats amid the storm that was unleashed by his site's decision to publish about 250,000 US diplomatic cables.
Since November 28, WikiLeaks has published the first of the embassy cables, creating an international firestorm as American diplomats' private assessments of foreign leaders and politics has been publicly aired.
The United States and other governments said the release of the documents broke their laws.
Stephens told the BBC on Sunday there was a risk that Swedish authorities could hand Assange over to their counterparts in the United States.
"Certainly in my mind it's very open about that" possibility, Stephens said, adding that he may "certainly" fight the Swedish arrest warrant on that basis.
One of the latest leaked cables meanwhile spoke of Google's decision to take down its search engine in China.
"A well-placed contact claims that the Chinese government coordinated the recent intrusions of Google systems," a cable dated earlier this year said.
"According to our contact, the closely held operations were directed at the Politburo Standing Committee level," it added, referring to the ruling body of the Chinese Communist Party.
A separate cable published Sunday said Saudi Arabia is the key source of funding for radical Islamist groups including Al-Qaeda, the Taliban, Hamas and Lashkar-e-Taiba.
Another said Tehran is a "dominant player" in Iraq using "all means of diplomacy, intelligence and economy" to get a pro-Iranian regime there.
The release of such cables marks the third major publication of secret US files by WikiLeaks this year, after the site had published tens of thousands of American military files on the Afghanistan and Iraq conflicts.
WikiLeaks meanwhile faces a new threat to its survival after the online payment service PayPal cut off the account used for donations to the website.
It has already been forced to switch its domain to Switzerland because its original web address was shut down by a US provider.
WikiLeaks on Sunday urged the public to set up mirror sites to safeguard its future.
In a message posted on the Internet, WikiLeaks noted that it "is currently under heavy attack" and called on the public to set up sites "to make it impossible to ever fully remove" it.
Elsewhere, the Swiss Post Office said it was carrying out checks on Assange's account with its banking arm, after doubts emerged over the Swiss address he gave.
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