Wakefield Trinity loanee was “disappointed and surprised” with manner of how his career with Hull FC came to an end, report the Yorkshire Post.
The prop joined Trinity on loan from the Black and Whites last week and is expected to make his debut against fellow relegation rivals Hull KR this weekend.
Before the move, the 29-year-old had spent his entire career with Hull and was their second-longest serving player.
Despite being out of contract at the end of the year, though, he said his exit was still unexpected.
“It was quite surprising (not getting offered a deal),” Green said. “I didn’t hear a lot from them and as time went on it was a bit disappointing but that’s how sport goes at times.
“I feel like I’m playing the best rugby I’ve ever played at the moment and it’s not ideal how this has happened. But I have to look after myself and my family and Hull couldn’t do that.
“I was playing regularly up to about three or four weeks ago and then the game-time started getting inconsistent which is not what I needed at this time of year.
“I’m off contract and needed to secure my future. I spoke to (coach) Lee (Radford) and he was reluctant at first to let me go but then they must have had a sit down and allowed me to move.
“At the moment, it’s just a loan deal but with a view of looking at next year so, for now, me and Wakefield both get chance to look at each other.”