The 31-year-old still has a year to run on his contract but has slipped down the pecking order following the recent arrivals of Simon Ramsden and Jon Bateson from Rochdale and Blackburn respectively.
Arnison told the club's official website: "I knew the manager was bringing in a right-back for competition but when two came in it was time for me to move on.
"I don't want to leave the club but things don't always work out as you want. I'm 31, nearly 32, and at my age I just want to be playing.
"I've spoken to the gaffer and he knows the situation. If I can find a club, and it's amicable for both parties, then I will look to go somewhere and hopefully play regularly again."
He added: "Nothing's really happening at the moment. I'm just training and working hard and waiting to see if something will come off."