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.
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