A legal clerk will present the case to three Court of Appeal judges in Stockholm on Friday, and they will "most likely announce their ruling next week," a clerk told AFP.
The judges will decide whether to grant Assange's request to hear legal arguments on the European arrest warrant issued by Swedish prosecutors in 2010.
Prosecutors want to question him about the rape allegation, which he denies.
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.
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 found on May 25, "contrary to the UN Working Group on Arbitrary Detention, that Julian Assange's stay at Ecuador's embassy in London 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".
Swedish prosecutor Marianne Ny told reporters Wednesday she was waiting to hear from Ecuador about when an interrogation with Assange could take place in the embassy.
"We are waiting now to be told how and when an interview can take place and if we will be allowed to be present when it is being held," Ny said.
Ecuador said on August 11 a date would be set in "the coming weeks."
Critical questions
Quito has insisted that Sweden submit its questions for Assange in writing, and an Ecuadoran prosecutor would conduct the interrogation.
It is not yet known whether the Swedish prosecutor will be allowed to be present.
Ny defended herself against critical questions from reporters about why the case has dragged on since 2010 without any progress, insisting that Assange was to blame for the delays.
"Mr Assange hasn't made himself available, which follows from the proceedings in Swedish courts," she said.
She suggested the case against him was strong.
"I don't want to go into how strong the evidence is. I can note that all of the courts that have examined this case have concluded that there is reasonable cause to suspect a crime has been committed," she said.
