Ola Bini was detained at Quito Airport in April while he was awaiting a flight to Japan, but has yet to be formally charged for any crime.
The 36-year-old programmer has been accused by the country's President Lenín Moreno of taking part in an espionage network organised by WikiLeaks founder Julian Assange, and the interior minister María Paula Romo has said he is suspected of hacking.
Dag Gustafsson, Bini's father, told SVT that his lawyer had applied for him to be released on bail.
“According to our son's lawyers all the legal prerequisites are place for bail to be accepted,” he said.
“Getting released on bail would be a way for him to be able to stay out while the investigation carries on and we would get him out of that terrible prison.”
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Gustafsson said he was hopeful that his son would eventually be freed.
“Somewhere inside there's a hope and a belief that all this is going to sort itself out,” he said. “But we were enormously disappointed after the last court session which ruled he should stay in custody.”
The ordeal has taken its toll on his son, he said.
“He isn't in a good place psychologically. But we will continue to battle so that all this ends well,” he said.
Bini's parents have confirmed that their son is a good friend of the Wikileaks founder and that he visited him at the Ecuadorean embassy several times. They deny, however, that Bini was officially involved in any Wikileaks activities.
According to international media reports, the 36-year-old Bini moved to Ecuador in 2013 as part of his work as a consultant for a US-based tech company that had contracted with the Ecuadorean government.