The 45-year-old Australian denies the 2010 allegations which he fears will see him extradited to the United States and tried over the leaking of hundreds of thousands of secret US military and diplomatic documents.
He has been holed up at the Ecuadoran embassy in London since 2012 and risks being arrested by British police if he steps out of the building.
Friday is the deadline for the public prosecutor's office to either renew or lift Assange's arrest warrant before a Stockholm court.
Assange's Swedish lawyer last month filed a new motion demanding that the arrest warrant be lifted after US Attorney General Jeff Sessions said in April that arresting Assange would be “a priority”.
“This implies that we can now demonstrate that the US has a will to take action… this is why we ask for the arrest warrant to be cancelled so that Julian Assange can fly to Ecuador and enjoy his political asylum,” lawyer Per Samuelsson told AFP at the time.
The Swedish prosecutor in charge of the investigation, Marianne Ny, is due to address a news
conference at 12:00 local time (1000 GMT) on Friday. According to Swedish media, she will comment on whether the investigation will continue or close but not if he is to be prosecuted. Neither Assange's lawyers nor the lawyer of his alleged victim could be reached for comment on Thursday.
The accusation against Assange dates from August 2010 when the alleged victim, who says she met him at a WikiLeaks conference in Stockholm a few days earlier, filed a complaint.
She accuses him of having sex with her as she slept without using a condom despite repeatedly having denied him unprotected sex.
“I am entirely innocent,” Assange wrote in a 19-page testimony released in December 2016.
He argues that the sex was consensual and that the accusations are “politically motived”.
The investigation has suffered from endless procedural complications since it began. The statute of limitations on the rape allegation expires in August 2020.
In a letter sent to the Swedish government on May 8, Ecuador condemned “the obvious lack of progress” in the investigation despite Swedish officials questioning Assange at the embassy in November 2016.
“It is extremely worrying that six months after the hearing at the Embassy of Ecuador in the United Kingdom, the Swedish prosecutor's office has not yet decided on the judicial situation of Julian Assange,” the Ecuadoran Foreign Ministry said in the letter seen by AFP.
Ecuador demands that Sweden either charges Assange or drops the investigation.
Swedish judges have refused to take into account the opinion of the UN Working Group on Arbitrary Detention, which in February 2016 said Assange was effectively “arbitrarily detained” by Sweden and Britain and called for the warrant to be annulled.