Raul is set to bring an end to a glittering career that included a 16-year spell with Real Madrid, where he won six league titles and three Champions League winner's medals. He was also the club's record goalscorer until Cristiano Ronaldo surpassed him earlier this season.
After spells with Schalke and Al Sadd, Raul joined the Cosmos at the end of 2014 and has the chance to go out on a high when they take on Ottawa Fury in the final of the North American Soccer League on Sunday.
"It was great to have Raul in our squad as an ambassador. He has been an example on and off the pitch," Savarese told AS.
"He's well-known [in the United States]. Very few players are as respected as Raul.
"Raul will do whatever he wants [in retirement]. He'll be what he wants. Whatever path he chooses he will be ready for personal success.
"I've no doubt he'll continue to be linked to the sport. I'm sure that football will always be linked to him. The feeling of the fans towards him is a result of his strong bond with football.
"Raul is a very demanding player. Every game is a final for him. He has contributed a lot to achieve important things."
It will also be the final match for Raul's Cosmos team-mate Marcos Senna, who won Euro 2008 with Spain.
"There is great admiration for both because they are very good professionals," Savarese added. "The Cosmos have grown and they're part of that.
"More than telling my grandchildren I coached Raul, I'll say I coached one of the greatest people I've ever met. And it's the same with Senna."