US prosecutors are set to approve the request, paving the way for Patel's arrest, the Herald Sun newspaper reported Thursday.
He will face the local court at Portland in Oregon where he currently lives and if the court grants an extradition warrant, Australian police could escort the surgeon or he could return to Queensland by himself.
In Australia, patient support group advocate Beryl Crosby said she was "over the moon".
"It's something we've waited a long time for. When it happens I will probably cry," Crosby said.
"I'm going to open a bottle of champagne I've kept, we're (Crosby and other victims) going to pop that," she added.
Patel, 57, dubbed 'doctor death' in Australia, faces charges relating to the deaths of 17 patients during his stint as director of surgery at the Bundaberg Base Hospital in Queensland between 2003 and 2005.
After the scandal surfaced, he fled to the US from where he had come to Australia.