Scotland Yard said they had served a "surrender notice" on the 40-year-old Australian requiring him to attend a police station, adding that failure to do so would make him further liable to arrest.
Assange faces extradition to Sweden over sex crime allegations, having exhausted his options under British law when the Supreme Court overturned his appeal against extradition earlier this month.
Fearing Stockholm would pass him on to the United States, he sought refuge at Ecuador's embassy in London on June 19, asking the South American country for political asylum.
Scotland Yard has "served a surrender notice upon a 40-year-old man that requires him to attend a police station at date and time of our choosing," a spokesman said.
"This is standard practice in extradition cases and is the first step in the removal process."
"He remains in breach of his bail conditions. Failing to surrender would be a further breach of conditions and he is liable to arrest."
It is understood that officers from Scotland Yard's extradition unit delivered a note to the embassy saying Assange has to present himself to a nearby police station at 11:30am Friday, the domestic Press Association news agency said.
Citing sources, PA said a letter was also delivered for Assange.
The embassy declined to comment on the serving of the police notice.
Assange fears that from Sweden he will be extradited to the United States to face possible espionage charges, after releasing more than 250,000 US diplomatic cables on the WikiLeaks anti-secrecy website.
Following a lengthy series of legal challenges that ran out earlier this month, he was given until June 28th to make a final appeal to the European Court of Human Rights, at which point extradition procedures in Britain could commence.
His lawyer was unavailable for comment on Thursday, while a spokesman for WikiLeaks told AFP he had talked to Assange on Wednesday, but declined to comment on whether an appeal to the ECHR had been made.
Ecuador's President Rafael Correa met with his envoy to London and other top officials to discuss Assange's request on Monday.
"The request for political asylum is being examined along with all the political implications it will have, including for Mr Assange," said Foreign Minister Ricardo Patino, adding that no timeframe had been set for a decision.
He is already in breach of his bail conditions, which state he must be at a given address between 10pm and 8am.
But while he remains in the embassy he is protected by diplomatic immunity and isbeyond the reach of British authorities.
The Ecuadorian embassy is a flat in a mansion block in the plush Knightsbridge district. It is located across the street from the well-known Harrods department store.