But Adams told talkSPORT: "I'm not sure Wayne Rooney could handle London, to be completely honest. That would be a massive risk for me.
"I don't think it's a question of finances. I think it's his temperament and mentality. London is a different animal. I think it takes a different type of player [to handle it].
"I think Wayne is unquestionably a super player and I'd love to see him at the Arsenal. Technically he's a fantastic player but I'm not sure about him mentally, off the pitch, and his professionalism.
"I know Sir Alex Ferguson has dealt with Wayne brilliantly over the last few years and I'm sure Arsene could handle him, but I'm not sure. I wouldn't like to spend my money on Wayne."