The godman is wanted by authorities in India for suspected child trafficking and sexual offences.
Reports quoting a top diplomat said, Nithyananda did visit Ecuador as a tourist in July 2018 and he was granted a temporary visa in October.
Jaime Marchan Romero said Nithyananda's application for refugee status and international protection status were rejected.
The diplomat denied reports that the godman had set up his own nation on Ecuadoran territory. He said such stories were sourced from his website kailaasa.org and urged Indian media to refrain from linking the godman to Ecuador.
A separate report said Nithyananda is believed to have fled to Haiti.
A court in India has ordered law enforcement to provide details of his whereabouts by December 12. The court also wanted to know the reasons for the delay in locating him, the report said.