The 50-year-old spent close to two decades in North London after breaking into the Gunners' first-team ranks, winning a total of 10 major honours.
Adams bowed out on a high by winning a league and cup double in 2002, but he has now revealed that Wenger blocked his return to the club in a coaching capacity, which he believes could be down to his outspoken personality.
"Perhaps Arsene thought I might be too challenging for him," he said in his autobiography, serialised in The Sun. "He seemed to like an assistant such as Pat Rice or Steve Bould, both great club men who were not going to ruffle feathers. Arsene is so dominant that he was probably not going to like it if I said, 'We're conceding bad goals, I'm going to take the back four today and organise them.'
"Because Arsene is essentially not a coach - and that is the second reason why I believe he didn't want me. Back in the day I said in an interview coaching wasn't Arsene's strong point. Actually in the original draft, I said he couldn't coach his way out of a paper bag.
"And though I modified that in the final article, it didn't go down well. It all left me feeling that I would never get a chance in any capacity while Arsene was there. Much as I respected him for his long and successful tenure, my occasional willingness to pass comment on him and the team probably counted against me."
Adams was placed in charge of La Liga club Granada in April, but was unable to stop the club's slide into the second tier of Spanish football.