Davis sang the praises of Oxlade-Chamberlain after Gunners winger marked his competitive England debut with a polished performance that was reminiscent of Manchester United ace Rooney when he starred for England at Euro 2004.
"I thought that Alex did really well against France and that’s all because he is so similar to Wayne Rooney," Davis told Goal.com. "He has a Wayne Rooney-esque fearlessness about his game that means that he just goes out and does his stuff.
"He is so fearless and it’s because he plays without fear is so reminiscent of what Wayne Rooney was like when he came on to the scene with Everton and England at Euro 2004.
"Alex is playing like Rooney did. I don’t think anything will ever faze him. He just goes out and gets on with it. There are no inhibitions that seem to be weighing him down."
The 18-year-old former Southampton player earned his third England cap against France and Davis believes he will prosper under Three Lions manager Roy Hodgson.
"He is a tremendously talented player but he showed that he will not be fazed by anything by the way he performed against France and he has done the same when he has been playing for Arsenal as well," Davis added.
"Nothing seems to daunt him at all and that is great for England. He is never afraid of being in possession, he never hides, he is always willing to run at opponents and he is never scared of having a shot.
"His body language and his overall play show that he is a very confident lad and he never let anyone down when he had the ball at his feet or when he had to work hard off the ball.
"They have got a really special talent out there and Roy Hodgson will get the best out of him because he is an educationalist who feels strongly about the merits of coaching and that shows Alex is in good hands."
Oxlade-Chamberlain was preferred to Liverpool winger Stewart Downing and Davis welcomed the surprise move by Hodgson.
"It was a bold move and Roy has to be applauded for picking him rather than Stewart Downing because Alex gives his England team an element of surprise with his pace and his vibrancy," Davis continued.
"I know it was Alex's competitive debut for England but he looked ever so composed and so comfortable out there and he showed to prove that he will be able to stay in the side. That was a really promising performance from Alex and I'm sure there is more to come not just now but in the long-term as well."
Davis was pleased with the 1-1 Group D draw that saw Samir Nasri cancel out Joleon Lescott's header but is concerned about the lack of a goal-scoring threat.
"All in all I was really pleased for Roy and I was pleased for the team that they did so well and that draw is a good platform for the rest of the tournament," said Davis, who is now a coach for the Professional Footballers' Association.
"It was encouraging but my only fear is about where the goals are going to come from. If you take the set-plays out of the equation when Rooney is not playing then it is difficult to see this England team scoring from open play. But it’s a case of so far so good."