The 26-year-old made a big impact at the Rhinos after joining them, initially on loan, from NRL club Penrith in July, helping them win nine of their last 10 matches of the season to comfortably retain their Super League status.
Segeyaro officially took up a two-year contract in September, removing a get-out clause at the same time, but has stated his desire to remain in Australia, where he is enjoying an extended off-season break.
"I wouldn't say I was pressured into taking up an option to re-sign with Leeds, but I certainly didn't have the support network I lean on when I make key life decisions," Segeyaro was quoted as saying by News Corp Australia.
"I told them I can't make the decision to take up the option without sitting down with my family.
"But we had a deadline and I had to make a decision. That's what I've explained to Gary throughout this period."
"I want to get on with my life and unfortunately that doesn't include going back to the UK. I just can't do it."
But Hetherington has reiterated the club's stance that Segeyaro, who has been heavily linked with a move to NRL premiers Cronulla, is not for sale.
"The comments attributed to James have obviously come as a big disappointment and a surprise following my meeting with him and his manager Sam Ayoub last Wednesday," said Hetherington.
"When speculation first broke regarding Cronulla and their interest in James, I alerted both the RFL and NRL chief executives to the issue and the NRL confirmed a player cannot be registered with an NRL club whilst his registration sits with a Super League club, and in James' case he is registered with us and the RFL until the end of 2018.
"Interest in him from other NRL clubs has been reported but they know he is not for sale. However I have no doubt this has become a key issue.
"The integrity of our game is now on the line and I hope to have further discussions with senior officials from the RFL and NRL at the earliest opportunity."
Segeyaro is due back at Headingley in early January ahead of the start of the Super League season the following month.
