The Portuguese defender has faith that his compatriot, whom he considers the finest in his position, will eventually fully settle in Spain to become a mainstay for Real Madrid
The left-back made only 12 league starts in his first season in the Spanish capital, having played second-fiddle to Marcelo for much of the campaign.
However, the Brazilian is currently with his country competing in the Olympics, leaving Coentrao as first choice to begin pre-season.
Coentrao, at 24, heads into 2012-13 as a reigning Liga champion with Los Blancos, and Pepe has no doubts about his compatriot's quality or ability to contribute consistently.
"He's the best full-back in the world," Pepe said. "I believe Madrid bear the privilege of having him.
"Fabio doesn't have to show anything to anybody. He has a lot of attributes, a lot of qualities.
"He's young. He's shown that he is a great player. He's made the World Cup and the Euros. None of his capabilities are in doubt."
International colleagues with Portugal, Pepe and Coentrao moved to Madrid from Spain's Iberian neighbor. The 29-year-old centre-back made the jump in 2007, so has some insight into the transition.
"When I got here with Real Madrid, the truth is they responded very well," Pepe continued.
"I know that the people like me, they love me, they have a lot of warmth for me. I'm enchanted for that warmth and love they've shown.
"As for Fabio, he's a new guy. His career has always been in Portugal. He had a somewhat bad experience coming to Spain but I believe that presently he has an opportunity to be able to play for the best club in the world.
"I believe that Fabio has that patience. He will be working hard to succeed for Madrid. I believe that the warmth the people have given to me they will give to him."