The Scotland international has gradually fallen out of favour at the Britannia Stadium amid increased competition for places, starting just 10 Premier League matches last term.
With players such as Giannelli Imbula arriving for club record fees, it is becoming increasingly more difficult for Adam to get any game-time with the Potters and questions have been asked about his future.
Adam, however, admits he is happy to play a minor role at Stoke as he targets 15 to 20 starts next season.
“I’m happy at Stoke so I’m going to stay there. If you want to keep progressing you need to move with the times,” the midfielder told the Daily Record.
“I always say that when I’m not playing I’m disappointed but the manager has said he knows he can trust me to come off the bench, that I can give him something different and change the game for the team.”
“If I’m going to play a number of games, maybe start 15-20 a season, I’m happy with that.”
Stoke finished ninth in the Premier League table for a third successive time last season although many felt with increased spending at the club a higher finish would be on the cards.
Nevertheless, the football has improved under boss Mark Hughes and the club's stature across Europe has risen allowing them to attract the likes of Xherdan Shaqiri, Bojan Krkic and Ibrahim Afellay, with more big names sure to follow.