Brazilian Ambassador Sergio Florencia says he hopes Mr. Gutierrez's transfer to Brazil will take place as soon as possible.
Mr. Gutierrez fled to the embassy after he was removed from office Wednesday by the Ecuadorean Congress following a week of massive street protests against his administration.
Vice President Alfredo Palacio was sworn in to replace the ousted leader.
U.S Secretary of State Condoleezza Rice, in Lithuania for a meeting of NATO foreign ministers, Thursday urged Ecuadoreans to follow a constitutional process toward possible new elections.
The crisis began last December, when Mr. Gutierrez fired 27 of the 31 justices on the Supreme Court after accusing them of bias against him. The move prompted weeks of street protests.
Some information for this report provided by AFP and AP.