A report in the Australian media claims Segeyaro has told Rhinos he is reluctant to return to the club for next season.
The former NRL hooker of the year is currently in Australia and is due back at Leeds on January 3.
He joined Rhinos on loan from Penrith Panthers in July and was a key figure in turning Leeds’ season around.
Rhinos lost just one of their 10 games with Segeyaro in the team and he signed a two-year deal in September.
The club released an “update” last Wednesday stating that “James Segeyaro will remain at the club and is looking forward to next season with the Rhinos”.
Chief executive Gary Hetherington - who is in Australia and has met with the player - insisted Rhinos are not prepared to release Segeyaro from his contract.
But an interview with Segeyaro on the website of Brisbane’s Courier Mail claims he struggled to settle in England and is desperate to remain Down Under.
The article says Segeyaro informed Hetherington last Wednesday of his “reluctance to return and continue playing in the UK and for the club....”
In it, Segeyaro is quoted as saying he was grateful for the opportunity at Leeds, but he adds: “But it’s hard when it’s just you eating dinner by yourself within four walls, especially the type of person I am.
“You start missing home, you look on your phone and see your parents and friends, who I treat like family and you’re a million miles away.
“That’s probably when I started questioning; ‘why am I doing this’?”
Segeyaro is quoted as adding: “The last two weeks I spent over there I tried hard to get into the English culture as I was really struggling.
“But I’m from North Queensland and I was born to go outside all the time. I fish, swim, go camping, all my childhood was outside.
“I’m a person who likes to do a lot of things, be outside and active.
“I was trying to do that over in England, but it’s not me. Mentally, I wasn’t happy ... I found myself so lonely.
“I needed my friends and my family who are number one. Anyone that knows my story, knows how close my family and friends are to me.
“I missed them so much. I missed my friends and in the last two weeks, I was so homesick.
“As soon as I got home, it was like a relief. I was so happy.”
Of his playing future, Segeyaro - who has been linked with Aussie champions Cronulla Sharks - says: “I haven’t talked with any clubs nor have I signed with anyone, how can I anyway? I need to sort out this matter.
“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.
“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
“I have a clothing label business that I am working on and I’m focused on my business studies. My dream is to open a cafe in Cairns, sometime in the future.
“I’m due back with Leeds on January 3, but honestly I’m not even looking that far ahead, I’m just taking each day as it comes.”
A walk-out by Segeyaro would be potentially catastrophic for Rhinos leaving them searching for a replacement in a pivotal position little more than two months before the start of the new season.