The 41-year-old Australian sparked a huge diplomatic stand-off after taking refuge in the embassy in London to avoid extradition to Sweden over alleged sex offences.
Last week Ecuador granted political asylum to Assange, but the UK Government has insisted he will not be allowed free passage out of Britain and will be arrested if he steps outside the embassy.
WikiLeaks spokesman Kristinn Hrafnsson said he would not be providing any details of how the appearance by Assange – scheduled for 12 noon today – would take place, in the face of the possibility that he could be arrested.
With police saying officers will act in an "appropriate manner" if he makes an appearance, one possibility is Assange may speak from a balcony to avoid arrest.
Ecuadorian ministers have been enraged by suggestions the UK could enter the embassy by using a rarely cited part of the Diplomatic and Consular Premises Act 1987, allowing revocation of the building's diplomatic immunity.
The row over Assange is also to be discussed by foreign ministers from across the Americas next week.
The Organisation of American States (OAS)'s permanent committee voted to hold a meeting on Friday in Washington after Ecuador's decision to grant political asylum to Assange.
OAS secretary general Jose Miguel Insulza said the meeting would discuss "the problem posed by the threat or warning made to Ecuador by the possibility of an intervention into its embassy in London".
He added: "What is being proposed is that the foreign ministers of our organisation address this subject and not the subject of asylum nor whether it should be granted to Mr Julian Assange. That will be discussed between Great Britain and Ecuador. The issue that concerns us is the inviolability of diplomatic missions of all members of this organisation, something that is of interest to all of us."
UK Foreign Secretary William Hague has said that diplomatic immunity should not be used to harbour alleged criminals and that the case could go on for "some considerable time."
He said: "We will not allow Mr Assange safe passage out of the United Kingdom, nor is there any legal basis for us to do so."
However, Hague has also insisted there is no threat to "storm an embassy".
Assange denies the allegations of rape which have been made against him. His supporters say he fears being sent by Sweden to the United States, where he could face charges of sedition and espionage over the release of tens of thousands of secret US documents by the WikiLeaks site two years ago.
On Friday, Ecuador's president Rafael Correa said that his nation was not trying to undermine Sweden's attempts to question Assange and the that main reason was to prevent his extradition to a "third country".
He added: "In no way was it done to interrupt the investigations of Swedish justice over an alleged crime. In no way."
But the Swedish foreign ministry said it has summoned Ecuador's ambassador over the Latin American country's "unacceptable" decision to grant asylum.
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