Wenger has come under renewed criticism for his failure to make any significant signings during the transfer window with the Arsenal Supporters' Trust declaring it would be currently "inappropriate" to offer him a new contract.
Adams, who made 504 appearances for Arsenal between 1983 and 2002, believes that whoever replaces Wenger will be given a different role to the Frenchman.
"One hundred per cent I'd like to be Arsenal manager," Adams told Zapsportz.com
"Of course my heart says 'yes, yes, yes', but my head says 'can I win with this current team?' My answer is no, I can't and I am not sure anyone can.
"I would want assurances if I walk through the door, those assurances meaning I'm given the go ahead to build a new team.
"I would get my teeth into building a new team but to achieve that, you would need to spend.
"To keep hitting the top four and qualifying for the Champions League is great, and Arsene has done such a great job, but there is going to come a day, and that won't be far away, when Arsene leaves.
"For a long time he has been a one-man band, but that won't happen again. The next man appointed will be the head coach, not the manager."
Adams believes one of Arsenal's greatest failings is a wage structure that pays top players too little and average players too much and also questions his tactics.