Khan, who appeared in the court, offered to provide a 20,000-pounds surety to prevent the 39-year-old Australian from being remanded in custody in Britain over the claims, reports the Telegraph.
“I would pay 'whatever sum was required' to ensure he was granted bail. I am not here to make any kind of judgment on the Julian Assange as an individual as I do not know him and I have never met him," Jemima Khan the former wife of Imran Khan said outside the court.
"I am here because I believe in the principle of the human right to freedom of information and our right to be told the truth," she added.
Four others, including film director Ken Loach, joined Khan to raise the surety amount.
However, a district judge at City of Westminster Magistrates Court decided Assange was too much of risk as it emerged that there was no record he ever arriving in Britain.
During Tuesday's hearing, he was accompanied by officials from the Australian High Commission after asking for consular assistance.
Swedish officials want Wikileaks founder be extradited to answer questions over the alleged rape of one woman and molestation of another while he was in Stockholm this summer, claims repeatedly denied by him.
Assange's supporters believe his arrest is a political stunt to detract from the revelations being made on a daily basis on the Wikileaks website.