Assange, 40, is believed to still be inside the Ecuadorian Embassy here, where he has been holed up since applying for political asylum on June 19. The deadline for the surrender of the hacker-turned activist was July 7.
Ecuador has said it is considering Assange's asylum application.
The UK Supreme Court had dismissed his bid to reopen his appeal against extradition to Sweden on June 14.
Karin Rosander, a spokeswoman for Sweden's Prosecution Authority, confirmed earlier that July 7 was the expected deadline for Assange's surrender.
UK police say Assange is in violation of his bail by staying at the embassy, and that ignoring the notice to turn himself in is a further violation. However, they are unable to enter the embassy under diplomatic protocol.
Assange is seeking to avoid being sent to Sweden over claims of rape and sexual molestation. He was arrested in Britain in 2010 because Swedish authorities wanted to question him about the allegations, which he denies. His bail conditions included staying every night at the home of a supporter outside of London.
Two women have accused Assange of sexually assaulting them in August 2010, when he was visiting Sweden. He was arrested in Britain that December and has been fighting extradition ever since, saying the allegations are retribution for his organisation's disclosure of American secrets.
Assange alleges the moves to extradite him to Sweden are politically motivated and that the ultimate aim is for him to be handed over to US authorities.
Susan Benn, of the Julian Assange defense fund, said on June 29 that Assange would not honour a notice served to him by British police a day earlier requiring him to turn himself in to authorities.
Benn said the US had empaneled a grand jury in its goal to press charges against Assange. Turning himself in would have started a process that would end with Assange being extradited to the US, she was quoted as saying by CNN.
WikiLeaks, which facilitates the anonymous leaking of secret information, has published about 250,000 confidential US diplomatic cables, causing embarrassment to the government and others. It also has published hundreds of thousands of classified US documents relating to the conflicts in Iraq and Afghanistan.
