Gleeson, 32, tested positive for banned stimulant methylhexaneamine, given to him in an energy supplement supplied by conditioning coach Ben Cooper, while playing for Hull.
The incident saw Gleeson, Cooper and then Hull chief executive James Rule, now at Widnes, receive bans from the game following a lengthy investigation by UK Anti-Doping.
The ex Huddersfield, St Helens, Warrington and Wigan centre made his comeback last weekend, playing for troubled Salford as a trialist in their pre-season win over Swinton, and he is set to sign a two-year deal with the club once they find a buyer.
Gleeson told the Daily Star: “People obviously did not do their jobs right and the worse thing was what happened after. I have not spoken about it before because it did my head in. I was not happy but I have done my time and I’m now back and in better nick than I’ve ever been.
“It has been tough and I was gutted how it happened but I don’t think I’ve got anything to prove and now I just want to finish my career on a high.
“I had not spoken to anyone in the rugby world and never looked for anything until Salford had a chat.
“I was a bit bitter at first and did not want anything to do with it but time is a healer and I thought I’d be stupid not to. Since December, when I started training with Salford, I’ve enjoyed it and had a smile on my face. It’s been really good compared to what I have been through in the last couple of years.”