Adams won 10 major honours in a 19-year stay at the Gunners and went out in style in 2002 on the back of a league and cup double.
The 50-year-old, who is currently managing LaLiga side Granada, claims he tried to return to the club on four occasions in a coaching capacity, but was overlooked each time.
Adams, who has a statue outside the Emirates Stadium, reckons he is too big a character for Wenger and that counted against him.
Speaking in his autobiography Sober, serialised in the Sun, he said: "Perhaps Arsene thought I might be too challenging for him.
"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 is currently back in the dugout for the first time since 2011 but his SOS mission at Granada could not have gone worse as he has lost all six of his games in charge and been unable to prevent relegation.
Previous managerial spells in England with Wycombe and Portsmouth were also ill-fated.
Adams also claims that Manchester United tried to sign him on two occasions, first in 1991 and then again in 1996.
He added: "I turned them down both times because I was Arsenal through and through.
"At the time, the wages weren't going to be much better, and I was stuck in my drinking and the London life with my mates and family around me.
"I wouldn't have had the tools to cope up in Manchester on my own.
"The second United approach came in 96, in the autumn just five weeks after I had stopped drinking and in that period of uncertainty when Arsene Wenger was taking over from the sacked Bruce Rioch.
"I guess Sir Alex (Ferguson) might also have wanted me because, as well as feeling he might be strengthening United, he might be weakening Arsenal."
Source : PA