Adams believes that despite being a quality forward, Rooney may struggle with life in London if he joins either Arsenal or Chelsea during the close season.
He told The Mirror: "I'm not sure Wayne Rooney could handle London. That would be a massive risk for me.
"I don't think it's a question of finances, it's his temperament and mentality. London is a different animal. It takes a different type of player to handle it.
"Wayne is a super player and I would love to see him at Arsenal. But I'm not sure about him mentally, off the pitch and his professionalism. I wouldn't like to spend my money on Wayne."
The Gunners remain bookies' favourites to sign Rooney this summer, with Paris Saint-Germain also thought to be monitoring his situation closely.