The 39-year-old Australian was ordered held in custody by a judge at a hearing a week ago after surrendering himself to Scotland Yard to answer a Swedish arrest warrant.
Assange is wanted for questioning after two women accused him of sexual misconduct in separate encounters in Sweden over the summer. Lawyers for Assange say he denies the allegations and will contest the attempt to extradite him for questioning.
Assange's lawyer, Mark Stephens, said his client would offer to be electronically tagged and stay at an address known to the police.
"One's never going to count one's chickens until they're hatched, but I hope that in these circumstances the district judge will feel confident" granting bail, Stephens told Sky News.
He will be represented in court by Geoffrey Robertson, a former appeals judge at the U.N. Special Court for Sierra Leone who specializes in freedom of speech cases. Robertson's former clients include author Salman Rushdie.
Supporters were planning to protest Assange's detention outside the court, following a small rally on Monday outside Sweden's embassy in London.
Some of Assange's supporters suspect the extradition request has been motivated by WikiLeaks' decision last month to begin publishing its trove of about 250,000 secret U.S. diplomatic cables, something Swedish officials have denied.
No criminal charges have been filed against Assange in Sweden, the U.K. or the United States, the Australian's lawyer in the U.S. has said sheagainst her client.
The Department of Justice has denied they are planning on prosecuting Assange anytime soon. A Justice Department official told NBC News on Friday that legal action against Assange "is not imminent." The U.S. government is moving slowly because it wants to make sure the prosecution is on solid ground, officials said.
Assange remained defiant in comments from prison relayed Tuesday by his mother. Australia's Seven network said Christine Assange spoke to her son by phone for 10 minutes and asked him, at the network's request, whether it had been worth it.
"," the network quoted Julian Assange as saying. "I remain true to the ideals I have expressed. This circumstance shall not shake them. If anything, this process has increased my determination that they are true and correct."
The disclosures, which have continued unaffected since Assange was detained in prison, have offended some U.S. allies and angered its rivals. Officials in Washington claim some other countries have already curtailed their dealings with the U.S. government as a result.
At an hour-long court hearing last week, lawyer Gemma Lindfield - acting for Swedish police - said Assange is accused of rape, molestation and unlawful coercion.
She told the court one woman had accused Assange of pinning her down and refusing to use a condom during an encounter on Aug. 14 in Stockholm. That woman also accused of Assange of molesting her in a way "designed to violate her sexual integrity" several days later.
A second woman has accused Assange of having sex with her without a condom while he was a guest at her Stockholm home and she was asleep.
In Sweden, a person who has sex with an unconscious, drunk or sleeping person can be convicted of rape and sentenced to up to six years in prison.
Assange's Swedish lawyer, Bjorn Hurtig, claims the courts are stacked against defendants in sex cases in Sweden.
However, a 2009 European Commission-funded study found only 10 percent of sex offenses reported in Sweden result in a conviction.
Lawyers for Assange said they will make a new application Tuesday to have him freed on bail, and will offer to post a hefty bond with the court. Several high-profile Britons - including socialite Jemima Khan and filmmaker Ken Loach - have offered to contribute 20,000 pounds ($31,500) each.
A decision on whether to extradite Assange is expected to take several weeks. Both Assange and the Swedish government are entitled to appeal against the ruling if the judge rules against them.
Britain's government said Monday that the country's national security adviser believes government websites could be attacked in retribution if Assange is not released.
Government departments have been told they could be targeted by online "hacktivists," following attacks on companies including MasterCard Inc., Visa Inc. and PayPal Inc., which cut ties to the WikiLeaks site.
In his statement, Assange called those companies "instruments of U.S. foreign policy."
"I am calling on the world to protect my work and my people from these illegal and immoral attacks," he was quoted as saying.