Wenger won the title three times in his opening eight years in charge but has not got his hands on the trophy for the last 13 years.
Asked whether his former club could win the league under Wenger, Adams told Sky Sports News: "He's contracted for another 18 months, so you're asking me whether this squad can do it. I don't think they can, I think that's pretty obvious.
"But how long will he go on for now? How old is he, 67? He's already said retirement is death to him, so you can't see him retiring and there doesn't seem to be anything outside of the game for him. It wouldn't be beyond me to see him sign another extension for another couple of years as well."
Despite their title drought, Arsenal have impressed in the FA Cup in recent years, winning three of the last four trophies.