Supreme Court decisions cannot normally be appealed but the court has given Assange's lawyers two weeks to decide whether they will demand that the case be reopened, Stockholm News reported.
His lawyers argued that they had not gotten all information about the international conventions that the court based its decision on.
Tuesday's verdict involved whether the Swedish prosecutor who issued the arrest notification against Assange had the legal authority to do so.
The WikiLeaks founder is currently holed up in Ecuador's London embassy.
Ecuador's president has warned Britain against trying to enter the embassy to arrest Assange, who has been granted asylum.
Speaking on state television days after his government offered Assange political asylum, Ecuadorean President Rafael Correa said it would be "disastrous" for British police to storm the embassy compound to seize Assange, The Guardian reported Tuesday.
The British government is looking at its options as it tries to carry out an extradition request from Sweden where Assange has been charged with sexual assault.
Assange has denied the charges and said he fears Sweden will turn him over to the United States for publishing sensitive documents on the wars in Iraq and Afghanistan and diplomatic matters. Assange, however, hasn't been charged in relation to those acts.
"I think it would be suicidal for the United Kingdom," Correa said. "After that, the diplomatic premises of [Britain] in other territories could be violated all over the world."
British Foreign Office officials in Quito delivered a letter last week to the Ecuadorean government, claiming the Diplomatic and Consular Premises Act 1987 allowed them to revoke an embassy's diplomatic status.
Assange has been hiding in the Ecuadorean Embassy since mid-June. Despite Ecuador's offer of asylum, he can't leave the embassy compound for the airport because Britain has refused to give him safe passage, The Guardian said.
Correa said he hoped Friday's meeting of the Organization of American States would arm him with a strong backing from regional allies, the newspaper said.
"Remember that David beat Goliath. And with many Davids it's easier to bring down a number of Goliaths," he said. "So we're hoping for clear and coherent backing because this violates all inter-American law, all international law, the Vienna convention and all diplomatic traditions of the last, at least, 300 years on a global scale."