Arnold helped guide Greene to World Championship glory in the 400m hurdles in 2011, but after a disappointing season that saw him fail to make the final at the Commonwealth Games, the Welshman has decided to go in a different direction.
The 28-year-old told Sport Wales: "I could do with a change of scene so at the moment, I'm in search of a new coach.
"I've been in Bath for around five years and I feel that the last couple of years haven't gone my way. It can be a little bit depressing going to training when you're the only guy injured and training on his own.
"I'm getting great support form the people at British Athletics and I'm sure that I'll find something in the next couple of weeks - there's plenty of things going on behind the scenes."
Greene will be targeting an improved season in 2015, with qualification for the World Championship in Beijing being his main aim for the year.