Assange has always refused to travel to Stockholm for questioning over the allegation, which he denies, due to concerns Sweden will extradite him to the United States over WikiLeaks' release of 500,000 secret military files on the wars in Afghanistan and Iraq.
Friday's hearing will be the eighth time the European arrest warrant has been tested in a Swedish court, with all seven previous rulings having gone against him.
The 45-year-old Australian sought refuge in the Ecuadorian embassy in London in June 2012 after exhausting all his legal options in Britain against extradition to Sweden.
The hearing comes a day after WikiLeaks released medical records claiming Assange's mental health was at risk if he remained confined in the embassy.
"Mr Assange’s mental health is highly likely to deteriorate over time if he remains in his current situation.... It is urgent that his current circumstances are resolved as quickly as possible," said a report published by the organisation on Twitter.
The 27-page medical report accompanied by supporting documents is attributed to an unnamed "trauma and psychosocial expert" in London and dated December 11, 2015.
Assange's lawyers have urged Sweden to respect a non-binding legal opinion by the UN Working Group on Arbitrary Detention, which on February 5 ruled that his confinement in the Ecuadorian embassy amounted to arbitrary detention by Sweden and Britain.
A Stockholm district court, however, rejected the finding, ruling that "Julian Assange's stay in the embassy should not be considered a detention".
It said the arrest warrant against him needed to be maintained because "there is still a risk that he will abscond or evade justice".
The appeals court will announce its decision at 11 am (0900 GMT).
Interrogation in October
Ecuador announced earlier this week that Assange had agreed to answer questions from Swedish investigators at the embassy from October 17.
The Swedish Prosecution Agency had asked that their own investigators be allowed to interrogate Assange in person, but Quito denied that request.
Instead, the Swedish prosecutors will provide their questions in writing and an Ecuadorian prosecutor will conduct the questioning.
Swedish prosecutor Ingrid Isgren and police investigator Cecilia Redell will however be allowed to be present.
The Swedish prosecution agency has defended itself against criticism that it has let the case drag on since 2010 without any progress.
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Prosecutors to interview Assange in London
Among other things, prosecutors insisted that Assange travel to Sweden to answer the allegations, although they dropped that demand in March 2015 and agreed to allow the questioning to take place in London.
Prosecutor Marianne Ny has insisted Assange was to blame for the lengthy delays.
"Mr Assange hasn't made himself available, which follows from the proceedings in Swedish courts," she told reporters on September 7.
Assange has meanwhile maintained that he has been sufficiently accommodating to Swedish justice officials.
The statute of limitations on the rape allegation expires on August 17, 2020.
