"We hope to have an agreement soon ... We hope to have it well before Christmas," Swedish justice ministry official Cecilia Riddselius told AFP.
Swedish and Ecuadorian officials met in Stockholm for the first time on Monday to hammer out a general agreement for judicial cooperation between the two countries.
Riddselius stressed the agreement was not specifically linked to the Assange case.
"This is a general agreement about judicial help in criminal cases that will allow authorities in the respective countries to help each other," she said.
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Swedish prosecutors offered in March to question Assange in London, dropping their previous demand that he come to Sweden to answer to the 2010 allegations.
The offer was seen as providing the potential for a breakthrough in the case, which has been deadlocked for nearly five years.
But Quito refused to allow such a meeting until a bilateral judicial agreement was in place.
Swedish prosecutors dropped a sexual assault probe against Assange in mid-August after the five-year statute of limitations expired.
Assange, who faces arrest if he tries to leave the embassy, denies the allegations and insists the sexual encounters were consensual.
The embassy is under 24-hour police guard.
The 44-year-old Australian fears that if he leaves he could eventually face extradition to the United States and a trial over the leak of hundreds of thousands of classified military and diplomatic documents in 2010.
Today's talks were led by Sweden's secretary of state, Ann Linde, and Ecuador's Fernando Yepez Lasso.