Adams, who won four league titles and three FA Cups during a 19-year career with the Gunners, believes the club were wrong to replace outgoing chairman Peter Hill-Wood with Keswick.
Hill-Wood spent over three decades as chairman but the 77-year-old stepped down during the week due to health reasons and Adams feels the wrong successor was appointed.
"Chips is a great guy but not a very imaginative choice by the owner - and he is 73," Adams told The Sun.
"If they just wanted a figurehead, they should have gone for me. It would have been a better visionary decision than Chips.
"They should be lining up the new manager. Chief executive Ivan Gazidis is in a tricky situation and could do with some help."
The 46-year-old Adams retired from football in 2002 with many expecting the former centre-back, who collected 66 England caps during his career, to make a successful transition into management but largely unsuccessful spells at Portsmouth and Azerbaijan outfit Gabala followed.
Wenger is credited by many with extending Adams' playing career at the top level but the Frenchman has not guided Arsenal to any silverware in the last eight seasons and Adams reckons they are still a long way off achieving such goals.
"It's time that Arsenal won something again, even the FA Cup or League Cup. But I can't see it, to be honest," he added.
"They are still not good enough in certain areas of the team. And they are miles off the title."