The former Blancos striker believes the World Cup 2014 Golden Boot winner can survive in a high-pressure environment
The Colombia international sealed a "dream" move to Los Blancos from Monaco earlier this month on the back of his Golden Boot-winning exploits at this summer's World Cup in Brazil.
Consequently, expectations are high among Madrid fans - but Butragueno believes has the right mentality to deal with the pressure of proving his worth to the Santiago Bernabeu faithful.
"He is young and Real Madrid is a very demanding club," the former Blancos striker told reporters.
"Our fans are very loyal but, at the same time, they expect your best. Every game is like a test, so you have to play well. We have to win.
"So, it’s part of our culture, our history. We have to win a title. It’s what our fans expect.
"But [James] is a nice guy. I had the opportunity to meet with him during the presentation, and I think he’s down to earth. He’s looking forward to starting the season, to helping us. Then we’ll see.
"But, really, we are very optimistic about what [role] he can play for us. We think he’s very talented, a very gifted player."
Rodriguez claimed the Golden Boot after netting six goals in just five games for Colombia at Brazil 2014.