The 39-year-old Australian makes his second appearance at court in London since his detention one week ago under an international warrant sent out by Sweden.
His arrest came shortly after his whistle-blowing website started releasing tens of thousands of leaked US diplomatic cables, in a move that has infuriated Washington.
Supporters of Assange and his site are expected to protest outside the City of Westminster Magistrates Court, amid a growing backlash against his arrest.
Swedish authorities want to question Assange over allegations of rape and molestation made against him by two women in relation to incidents during his visit there in August.
Assange denies the allegations and his lawyers have condemned them as politically motivated. Swedish officials however have retorted that the allegations have nothing to do with WikiLeaks.
At a hearing last week, Assange was refused jailed as he was deemed a flight risk.
His legal team are to reapply for bail at Tuesday's hearing, where he will be represented by high-profile human rights lawyer Geoffrey Robertson.
Assange's British attorney, Mark Stephens, said a secret US grand jury had been set up in Virginia to work on charges that could be filed against the WikiLeaks founder.
Stephens said in an interview with Al Jazeera, citing unnamed Swedish authorities, that "there has been a secretly impaneled grand jury in Alexandria," Virginia, just outside Washington.
If the report proves true, it could mean an indictment of Assange is possible.
There has been a groundswell of support for Assange since his arrest.
A petition on campaigning website Avaaz, which condemns what it terms as the crackdown on WikiLeaks, had attracted more than 600,000 signatories by 0100 GMT Tuesday.
Computer hackers meanwhile have targeted companies that have withdrawn their commercial services from WikiLeaks, such as Amazon and PayPal.
The Stop The War Coalition, which is organising the protest outside court, claims the US government and its allies have built up a campaign against Assange which culminated in his detention "on dubious charges".
WikiLeaks began releasing the leaked US cables at the end of last month in a move that has infuriated Washington and which US President Barack Obama has denouncing it as "deplorable".
Various countries have also tried to close down the site, sending it jumping from server to server in a bid to stay online.
Assange's British lawyer, Mark Stephens, said Monday a secret US grand jury had been set up in Virginia to work on charges that could be filed against the WikiLeaks founder, in comments to broadcaster Al-Jazeera.